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Article | REF: AF1224 V1

Calculation of eigenvalues

Authors: Bernard PHILIPPE, Yousef SAAD

Publication date: October 10, 2008

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7. Singular value decomposition

Singular value decomposition (SVD) has important applications in a wide variety of scientific fields. This decomposition can be seen as a generalization of the spectral decomposition of a Hermitian matrix, which is a decomposition of A into a product of the form A = U DU H where U is unitary and D diagonal. However, the SVD decomposition exists for any matrix, even in the case of rectangular matrices.

Theorem 13

For any matrix A∈ℝm×n , there exist orthogonal matrices

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