EigenvalueDecomposition

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 + imu, 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 = VD*Inverse(V) depends upon V.cond().