EigenvalueDecomposition {Microsoft.VisualBasic.Math.LinearAlgebra.Matrix}

.NET clr documentation

EigenvalueDecomposition

Description

Eigenvalues and eigenvectors of a real matrix. If A is symmetric, then A = VDV' 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 AV = VD, 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 = VDInverse(V) depends upon V.cond().

Declare

            
# namespace Microsoft.VisualBasic.Math.LinearAlgebra.Matrix
export class EigenvalueDecomposition {
   # Return the block diagonal eigenvalue matrix
   D: NumericMatrix;
   # Return the imaginary parts of the eigenvalues
   ImagEigenvalues: double;
   # Return the real parts of the eigenvalues
   RealEigenvalues: double;
   # Return the eigenvector matrix
   V: NumericMatrix;
}

        

.NET clr type reference tree

1. use by property member D: NumericMatrix
2. use by property member V: NumericMatrix

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