Documentation API of the 'cern.colt.matrix.linalg.EigenvalueDecomposition' Java class
EigenvalueDecomposition
cern.colt.matrix.linalg

Class EigenvalueDecomposition

  • All Implemented Interfaces:
    Serializable


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

    If A is symmetric, then A = V*D*V' where the eigenvalue matrix D isdiagonal and the eigenvector matrix V is orthogonal.I.e. A = V.mult(D.mult(transpose(V))) and V.mult(transpose(V)) equals the identity matrix.

    If A is not symmetric, then the eigenvalue matrix D is block diagonalwith 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.mult(V) equals V.mult(D). The matrix V may be badlyconditioned, or even singular, so the validity of the equationA = V*D*inverse(V) depends upon Algebra.cond(V).

    See Also:
    Serialized Form

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