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BUILT-IN MATHEMATICA SYMBOL
SingularValueDecomposition
SingularValueDecomposition[m]
gives the singular value decomposition for a numerical matrix m as a list of matrices 
, 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.
SingularValueDecomposition[{m, a}, k]
gives the generalized singular value decomposition associated with the k largest singular values.
Details and Options
- 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
such that m can be written as u.w.Conjugate[Transpose[v]] and a can be written as ua.wa.Conjugate[Transpose[v]]. »
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