SingularValueDecomposition
 Usage
• SingularValueDecomposition[m] gives the singular value decomposition for a numerical matrix m. The result is a list of matrices {u, w, v}, where w is a diagonal matrix, and m can be written as u . w . Conjugate[Transpose[v]].
• SingularValueDecomposition[{m, a}] gives the generalized singular value decomposition of m with respect to a.
• SingularValueDecomposition[m, k] gives the singular value decomposition associated with the k largest singular values of m.
Notes
• The matrix m may be rectangular. • The diagonal elements of w are the singular values of m. • SingularValueDecomposition sets to zero any singular values that would be dropped by SingularValueList. • The option Tolerance can be used as in SingularValueList to determine which singular values will be considered to be zero. • u and v are column orthonormal matrices, whose transposes can be considered as lists of orthonormal vectors. • SingularValueDecomposition[{m, a}] gives a list of matrices {{u, ua}, {w, wa}, v} such that m can be written as u . w . Conjugate[Transpose[v]] and a can be written as ua . wa . Conjugate[Transpose[v]]. • New in Version 5. • Advanced Documentation.
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