Eig

Eigenvalues and eigenvectors of a real matrix. <P> 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. <P> 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().

Constructors

this
this(Mat2D!double A)

Check for symmetry, then construct the eigenvalue decomposition @param A Square matrix @return Structure to access D and V.

Members

Functions

getD
Mat2D!double getD()

Return the block diagonal eigenvalue matrix @return D

getImagEigenvalues
double[] getImagEigenvalues()

Return the imaginary parts of the eigenvalues @return imag(diag(D))

getRealEigenvalues
double[] getRealEigenvalues()

Return the real parts of the eigenvalues @return real(diag(D))

getV
Mat2D!double getV()

Return the eigenvector matrix @return V

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