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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 . . . . as a Compression Algorithm . . . . . . . . . . . . . . . . . . . Decomposition.

Contents 1 Singular Value Decomposition (SVD) 2 ... 1 is perpendicular to W, any unit vector in W will do as w 2. If not, choose w 2 to be the unit vector in Wperpendicular to the projection of v 1 onto W:Since v 1 was chosen to maximize jAv 1j2, it follows that jAw 1j2 jAv 1j2.

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