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  • 6: Spectral Theory
    https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_Theory
    This page discusses Eigenvalues and Eigenvectors in Spectral Theory, covering special matrices, diagonalization, applications, Markov matrices, dynamical systems, orthogonal diagonalization, singular ...This page discusses Eigenvalues and Eigenvectors in Spectral Theory, covering special matrices, diagonalization, applications, Markov matrices, dynamical systems, orthogonal diagonalization, singular value decomposition, special factorizations, and quadratic forms. It includes exercises for practice to enhance understanding of both theoretical and practical aspects of these concepts.
  • 8.6: The Singular Value Decomposition
    https://math.libretexts.org/Bookshelves/Linear_Algebra/Linear_Algebra_with_Applications_(Nicholson)/08%3A_Orthogonality/8.06%3A_The_Singular_Value_Decomposition
    \[\begin{aligned} P\Sigma _{A} & = \left[ \begin{array}{cccccc}\mathbf{p}_{1} & \cdots & \mathbf{p}_{r} & \mathbf{p}_{r+1} & \cdots & \mathbf{p}_{m}\end{array}\right] \left[ \begin{array}{cc} \begin{a...\[\begin{aligned} P\Sigma _{A} & = \left[ \begin{array}{cccccc}\mathbf{p}_{1} & \cdots & \mathbf{p}_{r} & \mathbf{p}_{r+1} & \cdots & \mathbf{p}_{m}\end{array}\right] \left[ \begin{array}{cc} \begin{array}{ccc} \sigma _{1} & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & \sigma _{r} \end{array} & \begin{array}{ccc} 0 & \cdots & 0 \\ \vdots & & \vdots \\ 0 & \cdots & 0 \end{array} \\ \begin{array}{ccc} 0 & \cdots & ~0 \\ \vdots & & \vdots \\ 0 & \cdots & ~0 \end{array} & \begin{array}{cc…
  • 11.7: Singular-value decomposition
    https://math.libretexts.org/Bookshelves/Linear_Algebra/Book%3A_Linear_Algebra_(Schilling_Nachtergaele_and_Lankham)/11%3A_The_Spectral_Theorem_for_normal_linear_maps/11.07%3A_Singular-value_decomposition
    The singular-value decomposition generalizes the notion of diagonalization.
  • 17.1: Singular Value Decomposition
    https://math.libretexts.org/Bookshelves/Linear_Algebra/Map%3A_Linear_Algebra_(Waldron_Cherney_and_Denton)/17%3A_Least_Squares_and_Singular_Values/17.01%3A_Singular_Value_Decomposition
    Singular values appear in many linear algebra applications, especially those involving very large data sets such as statistics and signal processing.

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