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OuterPseudoInverse

SingularValues

FilledSmallSquareSingularValues[m] gives the singular value decomposition for a numerical matrix m. The result is a list u, w, v, where w is the list of singular values, and m can be written as Conjugate[Transpose[u]].DiagonalMatrix[w].v.

FilledSmallSquareSingularValues[m, Tolerance -> t] specifies that singular values smaller than t times the maximum singular value are to be removed.

FilledSmallSquare The default setting Tolerance -> Automatic typically takes t to be where is the numerical precision of the input.

FilledSmallSquare With Tolerance->0 singular values which are exactly zero can be returned.

FilledSmallSquareu and v are row orthonormal matrices, which can be considered as lists of orthonormal vectors.

FilledSmallSquare The ratio of the largest to smallest singular value gives the condition number of m.

FilledSmallSquare See The Mathematica Book: Section 3.7.10.

FilledSmallSquare Implementation Notes: see section A.9.4.

FilledSmallSquare See also: PseudoInverse, QRDecomposition, SchurDecomposition, LUDecomposition.

FilledSmallSquare Related packages: LinearAlgebra`Cholesky`, Statistics`LinearRegression`.

Further Examples

OuterPseudoInverse