EigenvalueDecomposition
Jama

Class EigenvalueDecomposition

  • All Implemented Interfaces:
    Serializable


    public class EigenvalueDecompositionextends Objectimplements Serializable
    Eigenvalues and eigenvectors of a real matrix.

    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.times(D.times(V.transpose())) and V.times(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.times(V) equals V.times(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().

    See Also:
    Serialized Form
    • Constructor Detail

      • EigenvalueDecomposition

        public EigenvalueDecomposition(Matrix Arg)
        Check for symmetry, then construct the eigenvalue decomposition Structure to access D and V.
        Parameters:
        Arg - Square matrix
    • Method Detail

      • getV

        public Matrix getV()
        Return the eigenvector matrix
        Returns:
        V
      • getRealEigenvalues

        public double[] getRealEigenvalues()
        Return the real parts of the eigenvalues
        Returns:
        real(diag(D))
      • getImagEigenvalues

        public double[] getImagEigenvalues()
        Return the imaginary parts of the eigenvalues
        Returns:
        imag(diag(D))
      • getD

        public Matrix getD()
        Return the block diagonal eigenvalue matrix
        Returns:
        D

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