Public Class SingularValueDecomposition _
	Inherits Decomposition

public class SingularValueDecomposition : Decomposition

public ref class SingularValueDecomposition : public Decomposition

The singular value decomposition (SVD) of a matrix A rewrites the matrix in the form A= USV^T, where U and V are orthogonal matrices, and S is a diagonal matrix whose diagonal contains the singular values of the matrix.

QRDecomposition can operate in two modes. In overwrite mode, the original matrix is overwritten by the decomposition. In preserve mode, the original matrix is preserved, and a new matrix is created to hold the decomposition. You can set the mode through the Overwrite property.

SingularValueDecomposition inherits from LinearTransformation. This means you can use it to solve systems of linear equations. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(GeneralMatrix, Boolean) method. You can also calculate the determinant, the inverse, and an estimate for the EstimateConditionNumber().

In addition, the SingularValueDecomposition class provides some unique methods. The GetPseudoInverse() method calculates the pseudo-inverse of the matrix. This is a matrix A⁺ such that AA⁺A = A.

The managed implementation of the singular value decomposition is based on the LINPACK routine DSVDC. The native version uses the LAPACK routine DGESDD.

System.Object
  Extreme.Mathematics.LinearAlgebra.LinearTransformation
    Extreme.Mathematics.LinearAlgebra.Decomposition
      Extreme.Mathematics.LinearAlgebra.SingularValueDecomposition