ISingularValueDecomposition Interface

Singular Value Decomposition for a rectangular matrix.

Namespace: Altaxo.Calc.LinearAlgebra
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3261.0 (4.8.3261.0)

Syntax

public interface ISingularValueDecomposition

The ISingularValueDecomposition type exposes the following members.

Properties

	Name	Description
	Condition	Returns the condition number max(S) / min(S).
	Diagonal	Return the one-dimensional array of singular values.
	Norm2	Returns the Two norm.
	Rank	Returns the effective numerical matrix rank.

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Remarks

For an m-by-n matrix A with m >= n, the singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-n orthogonal matrix V so that A = U * S * V'. The singular values, sigma[k] = S[k,k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1]. The singular value decompostion always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.

Reference

Altaxo.Calc.LinearAlgebra Namespace