Linear Algebra

  1. Inner Products and Orthogonality
    1. Inner Product Spaces
      1. Definition of inner product
        1. Inner product axioms
          1. Examples of inner products
            1. Dot product in Rⁿ
              1. Matrix inner products
                1. Function inner products
                2. Norm induced by inner product
                  1. Distance and angles
                  2. Orthogonality
                    1. Orthogonal vectors
                      1. Orthogonal sets
                        1. Orthonormal sets
                          1. Properties of orthogonal sets
                            1. Orthogonal complements
                              1. Orthogonal decomposition
                              2. Orthogonal Projections
                                1. Projection onto a line
                                  1. Projection onto subspaces
                                    1. Projection matrices
                                      1. Properties of projections
                                        1. Best approximation theorem
                                        2. Gram-Schmidt Process
                                          1. Orthogonalization procedure
                                            1. Normalization step
                                              1. QR factorization
                                                1. Orthogonal matrices
                                                  1. QR decomposition algorithm
                                                    1. Applications of QR factorization
                                                  2. Least Squares Problems
                                                    1. Overdetermined systems
                                                      1. Normal equations
                                                        1. Least squares solutions
                                                          1. Geometric interpretation
                                                            1. Applications to curve fitting

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                                                          5. Linear Transformations

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                                                          7. Eigenvalues and Eigenvectors