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EvdT Class

Eigenvalues and eigenvectors of a real matrix.
Inheritance Hierarchy
SystemObject
  Altaxo.Calc.LinearAlgebra.FactorizationEvdT

Namespace: Altaxo.Calc.LinearAlgebra.Factorization
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
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public abstract class Evd<T> : ISolver<T>
where T : struct, new(), IEquatable<T>, IFormattable

Type Parameters

T
Supported data types are double, single, Complex, and Complex32.

The EvdT type exposes the following members.

Constructors
 NameDescription
Protected methodEvdTInitializes a new instance of the EvdT class
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Properties
 NameDescription
Public propertyD Gets or sets the block diagonal eigenvalue matrix.
Public propertyDeterminant Gets the absolute value of determinant of the square matrix for which the EVD was computed.
Public propertyEigenValues Gets or sets the eigen values (λ) of matrix in ascending value.
Public propertyEigenVectors Gets or sets eigenvectors.
Public propertyIsFullRank Gets a value indicating whether the matrix is full rank or not.
Public propertyIsSymmetric Gets or sets a value indicating whether matrix is symmetric or not
Public propertyRank Gets the effective numerical matrix rank.
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Methods
 NameDescription
Public methodEqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
Protected methodFinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
Public methodGetHashCodeServes as the default hash function.
(Inherited from Object)
Public methodGetTypeGets the Type of the current instance.
(Inherited from Object)
Protected methodMemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
Public methodSolve(MatrixT) Solves a system of linear equations, AX = B, with A EVD factorized.
Public methodSolve(VectorT) Solves a system of linear equations, Ax = b, with A EVD factorized.
Public methodSolve(MatrixT, MatrixT) Solves a system of linear equations, AX = B, with A EVD factorized.
Public methodSolve(VectorT, VectorT) Solves a system of linear equations, Ax = b, with A EVD factorized.
Public methodToStringReturns a string that represents the current object.
(Inherited from Object)
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Remarks
If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V*D*V' and V*VT=I. If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.Multiply(V) equals V.Multiply(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*Inverse(V) depends upon V.Condition().
See Also