Inicio > Recursos educativos > Tutoriales

Presentación
Introducción al Machine Learning
Algoritmos de clasificación
Validación
Preprocesamiento de datos
Ingeniería de características
Algoritmos de regresión
Ensamblado de algoritmos
Optimización de un modelo
Algoritmos no supervisados
Algoritmos de aprendizaje por refuerzo
Miscelánea

Mensaje de error

Deprecated function: Use of "static" in callables is deprecated in Drupal\user\Entity\Role::postLoad() (line 172 of core/modules/user/src/Entity/Role.php).

Drupal\user\Entity\Role::postLoad(Object, Array) (Line: 423)
Drupal\Core\Entity\EntityStorageBase->postLoad(Array) (Line: 353)
Drupal\Core\Entity\EntityStorageBase->loadMultiple(Array) (Line: 16)
Drupal\user\RoleStorage->isPermissionInRoles('access site in maintenance mode', Array) (Line: 112)
Drupal\Core\Session\UserSession->hasPermission('access site in maintenance mode') (Line: 105)
Drupal\Core\Session\AccountProxy->hasPermission('access site in maintenance mode') (Line: 83)
Drupal\redirect\RedirectChecker->canRedirect(Object) (Line: 120)
Drupal\redirect\EventSubscriber\RedirectRequestSubscriber->onKernelRequestCheckRedirect(Object, 'kernel.request', Object)
call_user_func(Array, Object, 'kernel.request', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.request') (Line: 145)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Deprecated function: Creation of dynamic property Drupal\mysql\Driver\Database\mysql\Select::$alterMetaData is deprecated in Drupal\Core\Database\Query\Select->addMetaData() (line 178 of core/lib/Drupal/Core/Database/Query/Select.php).

Drupal\Core\Database\Query\Select->addMetaData('entity_type', 'file') (Line: 115)
Drupal\Core\Entity\Query\Sql\Query->prepare() (Line: 80)
Drupal\Core\Entity\Query\Sql\Query->execute() (Line: 640)
Drupal\Core\Entity\EntityStorageBase->loadByProperties(Array) (Line: 63)
Drupal\Core\Entity\EntityRepository->loadEntityByUuid('file', 'insert-max_800_px-d4755b6a-f571-451a-8804-6332fa116ce6') (Line: 95)
Drupal\editor\Plugin\Filter\EditorFileReference->process('Recordemos que el producto escalar de los vectores puede obtenerse proyectando uno sobre otro y multiplicando el módulo (longitud) de la proyección por el módulo del vector sobre el que estamos proyectando. Por ejemplo, consideremos los siguientes dos puntos s1 y s2, representados por sus vectores:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0151.png"></a>

En este ejemplo, el módulo del vector s1 es 3.61, y el módulo del vector s2 es 2.24. 

Para el cálculo del producto escalar habría que proyectar uno de los vectores -s2, por ejemplo- sobre el otro:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0152.png"></a>

Con los valores mencionados, el módulo de la proyección es 1.94.

Por último, tendríamos que multiplicar dicha cifra (1.94) por el módulo de s1 (3.61), para obtener el producto escalar buscado: 7.
', 'es') (Line: 118)
Drupal\filter\Element\ProcessedText::preRenderText(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 88)
__TwigTemplate_a7d6005c89ae729617b9a0c2bccb1776->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 46)
__TwigTemplate_804f7948456cfe20e11a34c43439c7c2->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 43)
__TwigTemplate_bd990293b89f3b78c69fe0ee2f7828b5->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/contrib/classy/templates/field/field--text-with-summary.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('field', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Deprecated function: Creation of dynamic property Drupal\mysql\Driver\Database\mysql\Select::$alterTags is deprecated in Drupal\Core\Database\Query\Select->addTag() (line 149 of core/lib/Drupal/Core/Database/Query/Select.php).

Drupal\Core\Database\Query\Select->addTag('entity_query') (Line: 147)
Drupal\Core\Entity\Query\Sql\Query->prepare() (Line: 80)
Drupal\Core\Entity\Query\Sql\Query->execute() (Line: 640)
Drupal\Core\Entity\EntityStorageBase->loadByProperties(Array) (Line: 63)
Drupal\Core\Entity\EntityRepository->loadEntityByUuid('file', 'insert-max_800_px-d4755b6a-f571-451a-8804-6332fa116ce6') (Line: 95)
Drupal\editor\Plugin\Filter\EditorFileReference->process('Recordemos que el producto escalar de los vectores puede obtenerse proyectando uno sobre otro y multiplicando el módulo (longitud) de la proyección por el módulo del vector sobre el que estamos proyectando. Por ejemplo, consideremos los siguientes dos puntos s1 y s2, representados por sus vectores:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0151.png"></a>

En este ejemplo, el módulo del vector s1 es 3.61, y el módulo del vector s2 es 2.24. 

Para el cálculo del producto escalar habría que proyectar uno de los vectores -s2, por ejemplo- sobre el otro:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0152.png"></a>

Con los valores mencionados, el módulo de la proyección es 1.94.

Por último, tendríamos que multiplicar dicha cifra (1.94) por el módulo de s1 (3.61), para obtener el producto escalar buscado: 7.
', 'es') (Line: 118)
Drupal\filter\Element\ProcessedText::preRenderText(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 88)
__TwigTemplate_a7d6005c89ae729617b9a0c2bccb1776->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 46)
__TwigTemplate_804f7948456cfe20e11a34c43439c7c2->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 43)
__TwigTemplate_bd990293b89f3b78c69fe0ee2f7828b5->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/contrib/classy/templates/field/field--text-with-summary.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('field', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addMetaData('entity_type', 'file') (Line: 115)
Drupal\Core\Entity\Query\Sql\Query->prepare() (Line: 80)
Drupal\Core\Entity\Query\Sql\Query->execute() (Line: 640)
Drupal\Core\Entity\EntityStorageBase->loadByProperties(Array) (Line: 63)
Drupal\Core\Entity\EntityRepository->loadEntityByUuid('file', 'insert-max_800_px-d4755b6a-f571-451a-8804-6332fa116ce6') (Line: 124)
Drupal\editor\Plugin\Filter\EditorFileReference->process('Recordemos que el producto escalar de los vectores puede obtenerse proyectando uno sobre otro y multiplicando el módulo (longitud) de la proyección por el módulo del vector sobre el que estamos proyectando. Por ejemplo, consideremos los siguientes dos puntos s1 y s2, representados por sus vectores:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0151.png"></a>

En este ejemplo, el módulo del vector s1 es 3.61, y el módulo del vector s2 es 2.24. 

Para el cálculo del producto escalar habría que proyectar uno de los vectores -s2, por ejemplo- sobre el otro:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0152.png"></a>

Con los valores mencionados, el módulo de la proyección es 1.94.

Por último, tendríamos que multiplicar dicha cifra (1.94) por el módulo de s1 (3.61), para obtener el producto escalar buscado: 7.
', 'es') (Line: 118)
Drupal\filter\Element\ProcessedText::preRenderText(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 88)
__TwigTemplate_a7d6005c89ae729617b9a0c2bccb1776->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 46)
__TwigTemplate_804f7948456cfe20e11a34c43439c7c2->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 43)
__TwigTemplate_bd990293b89f3b78c69fe0ee2f7828b5->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/contrib/classy/templates/field/field--text-with-summary.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('field', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addTag('entity_query') (Line: 147)
Drupal\Core\Entity\Query\Sql\Query->prepare() (Line: 80)
Drupal\Core\Entity\Query\Sql\Query->execute() (Line: 640)
Drupal\Core\Entity\EntityStorageBase->loadByProperties(Array) (Line: 63)
Drupal\Core\Entity\EntityRepository->loadEntityByUuid('file', 'insert-max_800_px-d4755b6a-f571-451a-8804-6332fa116ce6') (Line: 124)
Drupal\editor\Plugin\Filter\EditorFileReference->process('Recordemos que el producto escalar de los vectores puede obtenerse proyectando uno sobre otro y multiplicando el módulo (longitud) de la proyección por el módulo del vector sobre el que estamos proyectando. Por ejemplo, consideremos los siguientes dos puntos s1 y s2, representados por sus vectores:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0151.png"></a>

En este ejemplo, el módulo del vector s1 es 3.61, y el módulo del vector s2 es 2.24. 

Para el cálculo del producto escalar habría que proyectar uno de los vectores -s2, por ejemplo- sobre el otro:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0152.png"></a>

Con los valores mencionados, el módulo de la proyección es 1.94.

Por último, tendríamos que multiplicar dicha cifra (1.94) por el módulo de s1 (3.61), para obtener el producto escalar buscado: 7.
', 'es') (Line: 118)
Drupal\filter\Element\ProcessedText::preRenderText(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 88)
__TwigTemplate_a7d6005c89ae729617b9a0c2bccb1776->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 46)
__TwigTemplate_804f7948456cfe20e11a34c43439c7c2->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 43)
__TwigTemplate_bd990293b89f3b78c69fe0ee2f7828b5->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/contrib/classy/templates/field/field--text-with-summary.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('field', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addMetaData('entity_type', 'file') (Line: 115)
Drupal\Core\Entity\Query\Sql\Query->prepare() (Line: 80)
Drupal\Core\Entity\Query\Sql\Query->execute() (Line: 640)
Drupal\Core\Entity\EntityStorageBase->loadByProperties(Array) (Line: 63)
Drupal\Core\Entity\EntityRepository->loadEntityByUuid('file', 'insert-max_800_px-e670001b-55a2-417f-aa09-9132690ed949') (Line: 95)
Drupal\editor\Plugin\Filter\EditorFileReference->process('Recordemos que el producto escalar de los vectores puede obtenerse proyectando uno sobre otro y multiplicando el módulo (longitud) de la proyección por el módulo del vector sobre el que estamos proyectando. Por ejemplo, consideremos los siguientes dos puntos s1 y s2, representados por sus vectores:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0151.png"></a>

En este ejemplo, el módulo del vector s1 es 3.61, y el módulo del vector s2 es 2.24. 

Para el cálculo del producto escalar habría que proyectar uno de los vectores -s2, por ejemplo- sobre el otro:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0152.png"></a>

Con los valores mencionados, el módulo de la proyección es 1.94.

Por último, tendríamos que multiplicar dicha cifra (1.94) por el módulo de s1 (3.61), para obtener el producto escalar buscado: 7.
', 'es') (Line: 118)
Drupal\filter\Element\ProcessedText::preRenderText(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 88)
__TwigTemplate_a7d6005c89ae729617b9a0c2bccb1776->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 46)
__TwigTemplate_804f7948456cfe20e11a34c43439c7c2->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 43)
__TwigTemplate_bd990293b89f3b78c69fe0ee2f7828b5->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/contrib/classy/templates/field/field--text-with-summary.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('field', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addTag('entity_query') (Line: 147)
Drupal\Core\Entity\Query\Sql\Query->prepare() (Line: 80)
Drupal\Core\Entity\Query\Sql\Query->execute() (Line: 640)
Drupal\Core\Entity\EntityStorageBase->loadByProperties(Array) (Line: 63)
Drupal\Core\Entity\EntityRepository->loadEntityByUuid('file', 'insert-max_800_px-e670001b-55a2-417f-aa09-9132690ed949') (Line: 95)
Drupal\editor\Plugin\Filter\EditorFileReference->process('Recordemos que el producto escalar de los vectores puede obtenerse proyectando uno sobre otro y multiplicando el módulo (longitud) de la proyección por el módulo del vector sobre el que estamos proyectando. Por ejemplo, consideremos los siguientes dos puntos s1 y s2, representados por sus vectores:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0151.png"></a>

En este ejemplo, el módulo del vector s1 es 3.61, y el módulo del vector s2 es 2.24. 

Para el cálculo del producto escalar habría que proyectar uno de los vectores -s2, por ejemplo- sobre el otro:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0152.png"></a>

Con los valores mencionados, el módulo de la proyección es 1.94.

Por último, tendríamos que multiplicar dicha cifra (1.94) por el módulo de s1 (3.61), para obtener el producto escalar buscado: 7.
', 'es') (Line: 118)
Drupal\filter\Element\ProcessedText::preRenderText(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 88)
__TwigTemplate_a7d6005c89ae729617b9a0c2bccb1776->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 46)
__TwigTemplate_804f7948456cfe20e11a34c43439c7c2->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 43)
__TwigTemplate_bd990293b89f3b78c69fe0ee2f7828b5->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/contrib/classy/templates/field/field--text-with-summary.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('field', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addMetaData('entity_type', 'file') (Line: 115)
Drupal\Core\Entity\Query\Sql\Query->prepare() (Line: 80)
Drupal\Core\Entity\Query\Sql\Query->execute() (Line: 640)
Drupal\Core\Entity\EntityStorageBase->loadByProperties(Array) (Line: 63)
Drupal\Core\Entity\EntityRepository->loadEntityByUuid('file', 'insert-max_800_px-e670001b-55a2-417f-aa09-9132690ed949') (Line: 124)
Drupal\editor\Plugin\Filter\EditorFileReference->process('Recordemos que el producto escalar de los vectores puede obtenerse proyectando uno sobre otro y multiplicando el módulo (longitud) de la proyección por el módulo del vector sobre el que estamos proyectando. Por ejemplo, consideremos los siguientes dos puntos s1 y s2, representados por sus vectores:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0151.png"></a>

En este ejemplo, el módulo del vector s1 es 3.61, y el módulo del vector s2 es 2.24. 

Para el cálculo del producto escalar habría que proyectar uno de los vectores -s2, por ejemplo- sobre el otro:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0152.png"></a>

Con los valores mencionados, el módulo de la proyección es 1.94.

Por último, tendríamos que multiplicar dicha cifra (1.94) por el módulo de s1 (3.61), para obtener el producto escalar buscado: 7.
', 'es') (Line: 118)
Drupal\filter\Element\ProcessedText::preRenderText(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 88)
__TwigTemplate_a7d6005c89ae729617b9a0c2bccb1776->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 46)
__TwigTemplate_804f7948456cfe20e11a34c43439c7c2->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 43)
__TwigTemplate_bd990293b89f3b78c69fe0ee2f7828b5->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/contrib/classy/templates/field/field--text-with-summary.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('field', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addTag('entity_query') (Line: 147)
Drupal\Core\Entity\Query\Sql\Query->prepare() (Line: 80)
Drupal\Core\Entity\Query\Sql\Query->execute() (Line: 640)
Drupal\Core\Entity\EntityStorageBase->loadByProperties(Array) (Line: 63)
Drupal\Core\Entity\EntityRepository->loadEntityByUuid('file', 'insert-max_800_px-e670001b-55a2-417f-aa09-9132690ed949') (Line: 124)
Drupal\editor\Plugin\Filter\EditorFileReference->process('Recordemos que el producto escalar de los vectores puede obtenerse proyectando uno sobre otro y multiplicando el módulo (longitud) de la proyección por el módulo del vector sobre el que estamos proyectando. Por ejemplo, consideremos los siguientes dos puntos s1 y s2, representados por sus vectores:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0151.png"></a>

En este ejemplo, el módulo del vector s1 es 3.61, y el módulo del vector s2 es 2.24. 

Para el cálculo del producto escalar habría que proyectar uno de los vectores -s2, por ejemplo- sobre el otro:
<a class="colorbox insert-colorbox" data-colorbox-gallery="gallery-node" data-insert-class="" data-insert-type="image" href="/sites/default/files/2023-03/tutorial_ml_0152.png"></a>

Con los valores mencionados, el módulo de la proyección es 1.94.

Por último, tendríamos que multiplicar dicha cifra (1.94) por el módulo de s1 (3.61), para obtener el producto escalar buscado: 7.
', 'es') (Line: 118)
Drupal\filter\Element\ProcessedText::preRenderText(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 88)
__TwigTemplate_a7d6005c89ae729617b9a0c2bccb1776->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 46)
__TwigTemplate_804f7948456cfe20e11a34c43439c7c2->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array, Array) (Line: 43)
__TwigTemplate_bd990293b89f3b78c69fe0ee2f7828b5->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/contrib/classy/templates/field/field--text-with-summary.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('field', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addTag('node_access') (Line: 51)
Drupal\book\BookOutlineStorage->loadMultiple(Array) (Line: 1021)
Drupal\book\BookManager->bookTreeCheckAccess(Array, Array) (Line: 701)
Drupal\book\BookManager->bookTreeBuild('828', Array) (Line: 567)
Drupal\book\BookManager->bookTreeAllData('828', Array, 7) (Line: 792)
Drupal\book\BookManager->bookTreeGetFlat(Array) (Line: 109)
Drupal\book\BookOutline->childrenLinks(Array) (Line: 403)
template_preprocess_book_navigation(Array, 'book_navigation', Array)
call_user_func_array('template_preprocess_book_navigation', Array) (Line: 287)
Drupal\Core\Theme\ThemeManager->render('book_navigation', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addMetaData('base_table', 'book') (Line: 52)
Drupal\book\BookOutlineStorage->loadMultiple(Array) (Line: 1021)
Drupal\book\BookManager->bookTreeCheckAccess(Array, Array) (Line: 701)
Drupal\book\BookManager->bookTreeBuild('828', Array) (Line: 567)
Drupal\book\BookManager->bookTreeAllData('828', Array, 7) (Line: 792)
Drupal\book\BookManager->bookTreeGetFlat(Array) (Line: 109)
Drupal\book\BookOutline->childrenLinks(Array) (Line: 403)
template_preprocess_book_navigation(Array, 'book_navigation', Array)
call_user_func_array('template_preprocess_book_navigation', Array) (Line: 287)
Drupal\Core\Theme\ThemeManager->render('book_navigation', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addTag('node_access') (Line: 51)
Drupal\book\BookOutlineStorage->loadMultiple(Array, 1) (Line: 831)
Drupal\book\BookManager->loadBookLinks(Array, 1) (Line: 823)
Drupal\book\BookManager->loadBookLink('3985') (Line: 419)
template_preprocess_book_navigation(Array, 'book_navigation', Array)
call_user_func_array('template_preprocess_book_navigation', Array) (Line: 287)
Drupal\Core\Theme\ThemeManager->render('book_navigation', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addMetaData('base_table', 'book') (Line: 52)
Drupal\book\BookOutlineStorage->loadMultiple(Array, 1) (Line: 831)
Drupal\book\BookManager->loadBookLinks(Array, 1) (Line: 823)
Drupal\book\BookManager->loadBookLink('3985') (Line: 419)
template_preprocess_book_navigation(Array, 'book_navigation', Array)
call_user_func_array('template_preprocess_book_navigation', Array) (Line: 287)
Drupal\Core\Theme\ThemeManager->render('book_navigation', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array) (Line: 446)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array) (Line: 479)
Drupal\Core\Template\TwigExtension->escapeFilter(Object, Array, 'html', NULL, 1) (Line: 74)
__TwigTemplate_94047fbdba6937b76a4479dfa1763452->doDisplay(Array, Array) (Line: 405)
Twig\Template->displayWithErrorHandling(Array, Array) (Line: 378)
Twig\Template->display(Array) (Line: 390)
Twig\Template->render(Array) (Line: 55)
twig_render_template('themes/custom/yg_aesthetic/templates/node.html.twig', Array) (Line: 384)
Drupal\Core\Theme\ThemeManager->render('node', Array) (Line: 433)
Drupal\Core\Render\Renderer->doRender(Array, ) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, ) (Line: 242)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 235)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Deprecated function: Return type of Drupal\google_analytics\Component\Render\GoogleAnalyticsJavaScriptSnippet::jsonSerialize() should either be compatible with JsonSerializable::jsonSerialize(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include() (line 10 of modules/contrib/google_analytics/src/Component/Render/GoogleAnalyticsJavaScriptSnippet.php).

include('/var/www/vhosts/interactivechaos.ovh/httpdocs/modules/contrib/google_analytics/src/Component/Render/GoogleAnalyticsJavaScriptSnippet.php') (Line: 578)
Composer\Autoload\ClassLoader::Composer\Autoload\{closure}('/var/www/vhosts/interactivechaos.ovh/httpdocs/modules/contrib/google_analytics/src/Component/Render/GoogleAnalyticsJavaScriptSnippet.php') (Line: 432)
Composer\Autoload\ClassLoader->loadClass('Drupal\google_analytics\Component\Render\GoogleAnalyticsJavaScriptSnippet') (Line: 372)
google_analytics_page_attachments(Array) (Line: 313)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}(Object, 'google_analytics') (Line: 405)
Drupal\Core\Extension\ModuleHandler->invokeAllWith('page_attachments', Object) (Line: 310)
Drupal\Core\Render\MainContent\HtmlRenderer->invokePageAttachmentHooks(Array) (Line: 288)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Deprecated function: Use of "static" in callables is deprecated in Drupal\user\Entity\Role::postLoad() (line 172 of core/modules/user/src/Entity/Role.php).

Drupal\user\Entity\Role::postLoad(Object, Array) (Line: 423)
Drupal\Core\Entity\EntityStorageBase->postLoad(Array) (Line: 353)
Drupal\Core\Entity\EntityStorageBase->loadMultiple() (Line: 126)
eu_cookie_compliance_page_attachments(Array) (Line: 313)
Drupal\Core\Render\MainContent\HtmlRenderer->Drupal\Core\Render\MainContent\{closure}(Object, 'eu_cookie_compliance') (Line: 405)
Drupal\Core\Extension\ModuleHandler->invokeAllWith('page_attachments', Object) (Line: 310)
Drupal\Core\Render\MainContent\HtmlRenderer->invokePageAttachmentHooks(Array) (Line: 288)
Drupal\Core\Render\MainContent\HtmlRenderer->prepare(Array, Object, Object) (Line: 132)
Drupal\Core\Render\MainContent\HtmlRenderer->renderResponse(Array, Object, Object) (Line: 90)
Drupal\Core\EventSubscriber\MainContentViewSubscriber->onViewRenderArray(Object, 'kernel.view', Object)
call_user_func(Array, Object, 'kernel.view', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.view') (Line: 174)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addMetaData('entity_type', 'node') (Line: 115)
Drupal\Core\Entity\Query\Sql\Query->prepare() (Line: 80)
Drupal\Core\Entity\Query\Sql\Query->execute() (Line: 167)
Drupal\book\Plugin\Block\BookNavigationBlock->build() (Line: 171)
Drupal\block\BlockViewBuilder::preRender(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, 1) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, 1) (Line: 160)
Drupal\Core\Render\Renderer->Drupal\Core\Render\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 159)
Drupal\Core\Render\Renderer->renderPlain(Array) (Line: 175)
Drupal\Core\Render\Renderer->renderPlaceholder('', Array) (Line: 665)
Drupal\Core\Render\Renderer->replacePlaceholders(Array) (Line: 550)
Drupal\Core\Render\Renderer->doRender(Array, 1) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, 1) (Line: 148)
Drupal\Core\Render\Renderer->Drupal\Core\Render\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 147)
Drupal\Core\Render\Renderer->renderRoot(Array) (Line: 279)
Drupal\Core\Render\HtmlResponseAttachmentsProcessor->renderPlaceholders(Object) (Line: 71)
Drupal\big_pipe\Render\BigPipeResponseAttachmentsProcessor->processAttachments(Object) (Line: 45)
Drupal\Core\EventSubscriber\HtmlResponseSubscriber->onRespond(Object, 'kernel.response', Object)
call_user_func(Array, Object, 'kernel.response', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.response') (Line: 202)
Symfony\Component\HttpKernel\HttpKernel->filterResponse(Object, Object, 1) (Line: 190)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addTag('node_access') (Line: 145)
Drupal\Core\Entity\Query\Sql\Query->prepare() (Line: 80)
Drupal\Core\Entity\Query\Sql\Query->execute() (Line: 167)
Drupal\book\Plugin\Block\BookNavigationBlock->build() (Line: 171)
Drupal\block\BlockViewBuilder::preRender(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, 1) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, 1) (Line: 160)
Drupal\Core\Render\Renderer->Drupal\Core\Render\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 159)
Drupal\Core\Render\Renderer->renderPlain(Array) (Line: 175)
Drupal\Core\Render\Renderer->renderPlaceholder('', Array) (Line: 665)
Drupal\Core\Render\Renderer->replacePlaceholders(Array) (Line: 550)
Drupal\Core\Render\Renderer->doRender(Array, 1) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, 1) (Line: 148)
Drupal\Core\Render\Renderer->Drupal\Core\Render\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 147)
Drupal\Core\Render\Renderer->renderRoot(Array) (Line: 279)
Drupal\Core\Render\HtmlResponseAttachmentsProcessor->renderPlaceholders(Object) (Line: 71)
Drupal\big_pipe\Render\BigPipeResponseAttachmentsProcessor->processAttachments(Object) (Line: 45)
Drupal\Core\EventSubscriber\HtmlResponseSubscriber->onRespond(Object, 'kernel.response', Object)
call_user_func(Array, Object, 'kernel.response', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.response') (Line: 202)
Symfony\Component\HttpKernel\HttpKernel->filterResponse(Object, Object, 1) (Line: 190)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addTag('node_access') (Line: 51)
Drupal\book\BookOutlineStorage->loadMultiple(Array) (Line: 1021)
Drupal\book\BookManager->bookTreeCheckAccess(Array, Array) (Line: 701)
Drupal\book\BookManager->bookTreeBuild('828', Array) (Line: 567)
Drupal\book\BookManager->bookTreeAllData('828', Array) (Line: 171)
Drupal\book\Plugin\Block\BookNavigationBlock->build() (Line: 171)
Drupal\block\BlockViewBuilder::preRender(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, 1) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, 1) (Line: 160)
Drupal\Core\Render\Renderer->Drupal\Core\Render\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 159)
Drupal\Core\Render\Renderer->renderPlain(Array) (Line: 175)
Drupal\Core\Render\Renderer->renderPlaceholder('', Array) (Line: 665)
Drupal\Core\Render\Renderer->replacePlaceholders(Array) (Line: 550)
Drupal\Core\Render\Renderer->doRender(Array, 1) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, 1) (Line: 148)
Drupal\Core\Render\Renderer->Drupal\Core\Render\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 147)
Drupal\Core\Render\Renderer->renderRoot(Array) (Line: 279)
Drupal\Core\Render\HtmlResponseAttachmentsProcessor->renderPlaceholders(Object) (Line: 71)
Drupal\big_pipe\Render\BigPipeResponseAttachmentsProcessor->processAttachments(Object) (Line: 45)
Drupal\Core\EventSubscriber\HtmlResponseSubscriber->onRespond(Object, 'kernel.response', Object)
call_user_func(Array, Object, 'kernel.response', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.response') (Line: 202)
Symfony\Component\HttpKernel\HttpKernel->filterResponse(Object, Object, 1) (Line: 190)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Drupal\Core\Database\Query\Select->addMetaData('base_table', 'book') (Line: 52)
Drupal\book\BookOutlineStorage->loadMultiple(Array) (Line: 1021)
Drupal\book\BookManager->bookTreeCheckAccess(Array, Array) (Line: 701)
Drupal\book\BookManager->bookTreeBuild('828', Array) (Line: 567)
Drupal\book\BookManager->bookTreeAllData('828', Array) (Line: 171)
Drupal\book\Plugin\Block\BookNavigationBlock->build() (Line: 171)
Drupal\block\BlockViewBuilder::preRender(Array)
call_user_func_array(Array, Array) (Line: 101)
Drupal\Core\Render\Renderer->doTrustedCallback(Array, Array, 'Render #pre_render callbacks must be methods of a class that implements \Drupal\Core\Security\TrustedCallbackInterface or be an anonymous function. The callback was %s. See https://www.drupal.org/node/2966725', 'exception', 'Drupal\Core\Render\Element\RenderCallbackInterface') (Line: 788)
Drupal\Core\Render\Renderer->doCallback('#pre_render', Array, Array) (Line: 374)
Drupal\Core\Render\Renderer->doRender(Array, 1) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, 1) (Line: 160)
Drupal\Core\Render\Renderer->Drupal\Core\Render\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 159)
Drupal\Core\Render\Renderer->renderPlain(Array) (Line: 175)
Drupal\Core\Render\Renderer->renderPlaceholder('', Array) (Line: 665)
Drupal\Core\Render\Renderer->replacePlaceholders(Array) (Line: 550)
Drupal\Core\Render\Renderer->doRender(Array, 1) (Line: 204)
Drupal\Core\Render\Renderer->render(Array, 1) (Line: 148)
Drupal\Core\Render\Renderer->Drupal\Core\Render\{closure}() (Line: 580)
Drupal\Core\Render\Renderer->executeInRenderContext(Object, Object) (Line: 147)
Drupal\Core\Render\Renderer->renderRoot(Array) (Line: 279)
Drupal\Core\Render\HtmlResponseAttachmentsProcessor->renderPlaceholders(Object) (Line: 71)
Drupal\big_pipe\Render\BigPipeResponseAttachmentsProcessor->processAttachments(Object) (Line: 45)
Drupal\Core\EventSubscriber\HtmlResponseSubscriber->onRespond(Object, 'kernel.response', Object)
call_user_func(Array, Object, 'kernel.response', Object) (Line: 142)
Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(Object, 'kernel.response') (Line: 202)
Symfony\Component\HttpKernel\HttpKernel->filterResponse(Object, Object, 1) (Line: 190)
Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object, 1) (Line: 81)
Symfony\Component\HttpKernel\HttpKernel->handle(Object, 1, 1) (Line: 58)
Drupal\Core\StackMiddleware\Session->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object, 1, 1) (Line: 191)
Drupal\page_cache\StackMiddleware\PageCache->fetch(Object, 1, 1) (Line: 128)
Drupal\page_cache\StackMiddleware\PageCache->lookup(Object, 1, 1) (Line: 82)
Drupal\page_cache\StackMiddleware\PageCache->handle(Object, 1, 1) (Line: 48)
Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object, 1, 1) (Line: 51)
Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object, 1, 1) (Line: 23)
Stack\StackedHttpKernel->handle(Object, 1, 1) (Line: 713)
Drupal\Core\DrupalKernel->handle(Object) (Line: 19)

Producto escalar de dos vectores

Recordemos que el producto escalar de los vectores puede obtenerse proyectando uno sobre otro y multiplicando el módulo (longitud) de la proyección por el módulo del vector sobre el que estamos proyectando. Por ejemplo, consideremos los siguientes dos puntos s1 y s2, representados por sus vectores:

En este ejemplo, el módulo del vector s1 es 3.61, y el módulo del vector s2 es 2.24.

Para el cálculo del producto escalar habría que proyectar uno de los vectores -s2, por ejemplo- sobre el otro:

Con los valores mencionados, el módulo de la proyección es 1.94.

Por último, tendríamos que multiplicar dicha cifra (1.94) por el módulo de s1 (3.61), para obtener el producto escalar buscado: 7.

Enlaces transversales de Book para Producto escalar de dos vectores

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Producto escalar de dos vectores

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