If A is symmetric, then A = V * D * V' and A = V * V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. If A is not symmetric, 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. The matrix V may be badly conditioned, or even singular, so the validity of the equation A=V*D*inverse(V) depends upon the condition of V.