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().

Origin : JAMA http://math.nist.gov/javanumerics/jama/ placed in public domain.

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

Return the eigenvector matrix
return  V

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

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

Return the block diagonal eigenvalue matrix
return  D