A Tutorial On The Singular Value Decomposition

Authors : Abdurrahman KARAMANCIOĞLU, Can ÖZDEMİR

Pages : 1-12

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Publication Date : 1996-06-30

Article Type : Research Paper

Abstract :An m y, n real matm A can be factored as ITWV , where V and V are orthonormal, and W is upper left diagonal. Thîs factorization is called Singular Vaîue Decomposilion (SVD). The matrlces U, W, and V are usefül in characterizing ıhe malrix A. in this manuscript geometric characterizations are emphasized. Geometric characîerizations are anaîyzed in terms ofsubspaces, matrix scaling, cmd norms. We also presenî a numerical viewpoint for SVD m orcfer to keep the maîerial setf-contained. in the last section we îreat a special problem where action ofîhe matrix A is restncted to a gıven subspace.
Keywords : Singular values, matrix decomposition, matrix