A Tutorial On The Singular Value Decomposition

Year 1996, Volume: 9 Issue: 1, 1 - 12, 30.06.1996

Abdurrahman Karamancıoğlu , Can Özdemir

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

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