﻿DoubleComplexEigDecomp Class

# DoubleComplexEigDecomp Class

Class DoubleComplexEigDecomp computes the eigenvalues and left and right eigenvectors of a general matrix, with preliminary balancing.
Inheritance Hierarchy
SystemObject
CenterSpace.NMath.CoreDoubleComplexEigDecomp

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

The DoubleComplexEigDecomp type exposes the following members.

Constructors
NameDescription
DoubleComplexEigDecomp
Default constructor. Constructs an empty eigenvalue decomposition.
DoubleComplexEigDecomp(DoubleComplexMatrix)
Construct a DoubleComplexEigDecomp instance for the given matrix.
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Properties
NameDescription
Cols
Gets the number of columns in the decomposed matrix.
EigenValues
Gets the computed eigenvalues.
IsGood
Returns true if the all the eigenvalues and eigenvectors were successfully computed; otherwise, false.
LeftEigenVectors
Gets the matrix of left eigenvectors.
NumberOfEigenValues
Gets the number of eigenvalues computed.
NumberOfLeftEigenVectors
Gets the number of left eigenvectors.
NumberOfRightEigenVectors
Gets the number of right eigenvectors.
RightEigenVectors
Gets the matrix of right eigenvectors.
Rows
Gets the number of rows in the decomposed matrix.
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Methods
NameDescription
Clone
Creates a deep copy of this eigenvalue decompostiion.
EigenValue
Returns the ith eigenvalue.
Factor
Computes all the eigenvalues and eigenvectors for the given square matrix.
FactorNoPreconditioning
Computes all the eigenvalues and eigenvectors for the given square matrix.
LeftEigenVector
Returns the ith left eigenvector.
RightEigenVector
Returns the ith right eigenvector.
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Remarks
Balancing a matrix means permuting the rows and columns to make it more nearly upper triangular, and applying a diagonal similarity transformation to make its rows and columns closer in norm and the condition numbers of its eigenvalues and eigenvectors smaller.