{"id":86,"date":"2025-09-20T01:58:46","date_gmt":"2025-09-20T01:58:46","guid":{"rendered":"https:\/\/itisallmath.com\/linear-algebra\/"},"modified":"2025-12-31T14:50:49","modified_gmt":"2025-12-31T14:50:49","slug":"linear-algebra","status":"publish","type":"page","link":"https:\/\/itisallmath.com\/es\/mathematics\/linear-algebra\/","title":{"rendered":"Linear Algebra"},"content":{"rendered":"
<\/div><\/div>\n\n\n\n
\n
\"\"<\/figure>\n\n\n\n

What are you going to learn?<\/h2><\/div>\n\n\n\n

Model and systematically solve systems of linear equations using matrix notation. Demonstrate factual knowledge of the fundamental concepts of spanning, linear independence, and linear transformations. Use matrix algebra to analyze and solve equations arising in many applications that require a background in linear algebra. Utilize vector space terminology and describe how closely other vector spaces resemble Rn. Dissect the action of a linear transformation into elements that are easily visualized using the basic concepts of eigenvectors and eigenvalues.<\/p>\n<\/div><\/div>\n\n\n\n

Content<\/h2><\/div>\n\n\n\n
\n
\n

Chapter 1. Vectors<\/strong><\/h3><\/div>\n\n\n\n
    \n
  1. Definition<\/li>\n\n\n\n
  2. Scalar Product<\/li>\n\n\n\n
  3. Norm of a Vectors<\/li>\n\n\n\n
  4. Parametric Lines<\/li>\n\n\n\n
  5. Planes<\/li>\n<\/ol>\n<\/div>\n\n\n\n
    <\/div>\n<\/div><\/div>\n\n\n\n
    \n
    \n

    Chapter 2. Matrices and Linear Equations<\/strong><\/strong><\/h3><\/div>\n\n\n\n
      \n
    1. Definition<\/li>\n\n\n\n
    2. Operations with Matrices<\/li>\n\n\n\n
    3. Row Operations<\/li>\n\n\n\n
    4. The Inverse Matrix<\/li>\n<\/ol>\n<\/div>\n\n\n\n
      <\/div>\n<\/div><\/div>\n\n\n\n
      \n
      \n

      Chapter 3. Vector Spaces<\/strong><\/strong><\/h3><\/div>\n\n\n\n
        \n
      1. Definition. Subspaces<\/li>\n\n\n\n
      2. Linear Combination, Linear Independence<\/li>\n\n\n\n
      3. Basis, Dimension<\/li>\n\n\n\n
      4. Finding the Basis of a Linear Space<\/li>\n\n\n\n
      5. Coordinates. Changes of Basis<\/li>\n<\/ol>\n<\/div>\n\n\n\n
        <\/div>\n<\/div><\/div>\n\n\n\n
        \n
        \n

        Chapter 4. Linear Mappings<\/strong><\/strong><\/h3><\/div>\n\n\n\n
          \n
        1. Definition. Linear Mappings<\/li>\n\n\n\n
        2. Kernel and Range of a Linear Transformation<\/li>\n\n\n\n
        3. Range and Linear Equations<\/li>\n\n\n\n
        4. Matrix Associated with a Linear Transformation<\/li>\n\n\n\n
        5. Change of Basis<\/li>\n<\/ol>\n<\/div>\n\n\n\n
          <\/div>\n<\/div><\/div>\n\n\n\n
          \n
          \n

          Chapter 5. Composition and Inverse Mappings<\/strong><\/strong><\/h3><\/div>\n\n\n\n
            \n
          1. Graphs Terminology<\/li>\n\n\n\n
          2. Digraphs and Connectivity Problems<\/li>\n<\/ol>\n<\/div>\n\n\n\n
            <\/div>\n<\/div><\/div>\n\n\n\n
            \n
            \n

            Chapter 6. Scalar Products and Ortogonality<\/strong><\/strong><\/h3><\/div>\n\n\n\n
              \n
            1. Inner Product. Length. Orthogonal Vectors. Triangle Inequality<\/li>\n\n\n\n
            2. Cauchy-Schwartz Inequality<\/li>\n\n\n\n
            3. Orthonormal Basis, Gram-Schmidt Process<\/li>\n<\/ol>\n<\/div>\n\n\n\n
              <\/div>\n<\/div><\/div>\n\n\n\n
              \n
              \n

              Chapter 7. Determinants<\/strong><\/strong><\/h3><\/div>\n\n\n\n
                \n
              1. Determinant of 2×2, 3×3 Matrices<\/li>\n\n\n\n
              2. Minors and Cofactors of a Square Matrix<\/li>\n\n\n\n
              3. Cofactor Theorem<\/li>\n\n\n\n
              4. Properties of Determinants<\/li>\n\n\n\n
              5. Cramer’s Rule<\/li>\n<\/ol>\n<\/div>\n\n\n\n
                <\/div>\n<\/div><\/div>\n\n\n\n
                \n
                \n

                Chapter 8. Eigenvectors and Eigenvalues<\/strong><\/strong><\/h3><\/div>\n\n\n\n
                  \n
                1. Definition<\/li>\n\n\n\n
                2. Diagonalization<\/li>\n\n\n\n
                3. Symmetric Matrices and Orthogonal Diagonalization<\/li>\n<\/ol>\n<\/div>\n\n\n\n
                  <\/div>\n<\/div><\/div>\n\n\n\n

                  Bibliography<\/h2><\/div>\n\n\n\n
                    \n
                  • Lang, S. Introduction to Linear Algebra<\/em><\/strong>. 2th ed, Springer, 2000.<\/li>\n\n\n\n
                  • Larson, R. Elementary Linear Algebra<\/em><\/strong>. 8th ed, Cengage Learning, 2017<\/em>.<\/li>\n<\/ul>\n\n\n\n

                    Bibliography<\/h2><\/div>\n\n\n\n
                      \n
                    • <\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"

                      What are you going to learn? Model and systematically solve systems of linear equations using matrix notation. Demonstrate factual knowledge […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":340,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"_uag_custom_page_level_css":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"wf_page_folders":[44],"class_list":["post-86","page","type-page","status-publish","hentry"],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"hd_qu_size2":false,"1536x1536":false,"2048x2048":false,"trp-custom-language-flag":false},"uagb_author_info":{"display_name":"carroyav02@gmail.com","author_link":"https:\/\/itisallmath.com\/es\/author\/carroyav02gmail-com\/"},"uagb_comment_info":0,"uagb_excerpt":"What are you going to learn? Model and systematically solve systems of linear equations using matrix notation. Demonstrate factual knowledge […]","_links":{"self":[{"href":"https:\/\/itisallmath.com\/es\/wp-json\/wp\/v2\/pages\/86","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/itisallmath.com\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/itisallmath.com\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/itisallmath.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/itisallmath.com\/es\/wp-json\/wp\/v2\/comments?post=86"}],"version-history":[{"count":5,"href":"https:\/\/itisallmath.com\/es\/wp-json\/wp\/v2\/pages\/86\/revisions"}],"predecessor-version":[{"id":1545,"href":"https:\/\/itisallmath.com\/es\/wp-json\/wp\/v2\/pages\/86\/revisions\/1545"}],"up":[{"embeddable":true,"href":"https:\/\/itisallmath.com\/es\/wp-json\/wp\/v2\/pages\/340"}],"wp:attachment":[{"href":"https:\/\/itisallmath.com\/es\/wp-json\/wp\/v2\/media?parent=86"}],"wp:term":[{"taxonomy":"wf_page_folders","embeddable":true,"href":"https:\/\/itisallmath.com\/es\/wp-json\/wp\/v2\/wf_page_folders?post=86"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}