﻿DoubleComplexGSVDecomp Class   # DoubleComplexGSVDecomp Class

Class DoubleComplexGSVDecomp computes the generalized singular value decomposition (GSVD) of a pair of general rectangular matrices. Inheritance Hierarchy
SystemObject
CenterSpace.NMath.CoreDoubleComplexGSVDecomp

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4 Syntax
```[SerializableAttribute]
public class DoubleComplexGSVDecomp```

The DoubleComplexGSVDecomp type exposes the following members. Constructors
NameDescription DoubleComplexGSVDecomp(DoubleComplexMatrix, DoubleComplexMatrix) Computes the general singular value decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) for two matrices A and B. U, V, and Q are computed. A and B must have the same number of columns. DoubleComplexGSVDecomp(DoubleComplexMatrix, DoubleComplexMatrix, Boolean, Boolean, Boolean) Computes the general singular value decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) for two matrices A and B, optionally computing U, V, and Q. A and B must have the same number of columns.
Top Properties
NameDescription ComputeQ Returns true if the matrix Q in the decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) was computed. ComputeU Returns true if the matrix U in the decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) was computed. ComputeV Returns true if the matrix V in the decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) was computed. D1 Gets the matrix D1 in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R) D2 Gets the matrix D2 in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R) IsGood Returns true if the decomposition was successfully computed. Returns false if the procedure failed to converge. Q Gets the matrix Q in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R) R Gets the matrix R in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R) RankOfATranspose_BTranspose Gets the effective numerical rank of (A' B'), where Z' denotes the conjugate transpose of the matrix Z and A and B are the decomposed matrices. U Gets the matrix U in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R) V Gets the matrix V in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R) Zero_R Gets the matrix (0 R) in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R) (0 R) is the matrix obtained by prepending columns of all zeros to the upper triangular matrix R.
Top Remarks
The GSVD computed for an m x n matrix A and a p x n matrix B has the form
U'AQ = D1(0 R), V'BQ = D2(0 R)
where U, V, and Q are orthogonal matrices, R is a nonsigular upper triangular matrix, D1 and D2 are diagonal matrices, and Z' denotes the transpose of the matrix Z. (0 R) is the matrix obtained by prepending columns of all zeros to the upper triangular matrix R. See Also

#### Reference

CenterSpace.NMath.Core Namespace