CADability dotNET
Assembly: CADability (in CADability.dll) Version: 1.1.4254.24737 (1.1.*)
Eigenvalues and eigenvectors of a real matrix.
Namespace: CADability.LinearAlgebraAssembly: CADability (in CADability.dll) Version: 1.1.4254.24737 (1.1.*)
Syntax
C# |
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[SerializableAttribute] public class EigenvalueDecomposition |
Visual Basic |
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<SerializableAttribute> _ Public Class EigenvalueDecomposition |
Visual C++ |
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[SerializableAttribute] public ref class EigenvalueDecomposition |
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.Multiply(D.Multiply(V.Transpose())) and
V.Multiply(V.Transpose()) equals the identity matrix.
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.cond().