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Contents1 Singular Value decomposition (SVD) Singular Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Singular Value decomposition (SVD) . . . . . . . . . . . . . . . . . . . . . Best RankkApproximations . . . . . . . . . . . . . . . . . . . . . . . . . Power Method for Computing the Singular Value decomposition . . . . . . Applications of Singular Value decomposition . . . . . . . . . . . . . . . . Component Analysis . . . . . . . . . . . . . . . . . . . . . a Mixture of Spherical Gaussians . . . . . . . . . . . . . Application of SVD to a Discrete Optimization Problem.

1 Singular Value Decomposition (SVD) The singular value decomposition of a matrix Ais the factorization of Ainto the product of three matrices A= UDVT where the columns of Uand Vare orthonormal and the matrix Dis diagonal with positive real entries.

  Decomposition

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