Linear Algebra

  1. Advanced Topics
    1. Symmetric Matrices and Spectral Theory
      1. Properties of symmetric matrices
        1. Spectral theorem for symmetric matrices
          1. Orthogonal diagonalization
            1. Principal axes theorem
              1. Quadratic forms
              2. Singular Value Decomposition
                1. Definition of singular values
                  1. SVD construction
                    1. Left singular vectors
                      1. Right singular vectors
                        1. Singular value matrix
                        2. Geometric interpretation
                          1. Applications of SVD
                            1. Matrix approximation
                              1. Data compression
                                1. Principal component analysis
                              2. Complex Vector Spaces
                                1. Complex numbers in linear algebra
                                  1. Complex vector spaces
                                    1. Hermitian inner products
                                      1. Hermitian matrices
                                        1. Unitary matrices
                                          1. Spectral theory for Hermitian matrices
                                          2. Jordan Canonical Form
                                            1. Generalized eigenspaces
                                              1. Jordan blocks
                                                1. Jordan canonical form
                                                  1. Computing Jordan form
                                                    1. Applications and significance

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                                                  7. Eigenvalues and Eigenvectors

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                                                  1. Foundations of Linear Systems