author: Nikolai V. Shokhirev 2004
Diagonalization of complex Hermitian matrix
Moore-Penrose Matrix Inverse (Pseudoinverse)
Input:
a - m x n arbitrary rectangular matrix; mn = min(m,n)
SVD: a = Sum(i=1,nm)[wi*|ui><vi|]
Pseudoinverse:
a˜ = Sum(j=1,k)[1/(wi+s)*|ui><vi|] wi > e; e, s >= 0; k <= mn
Moore-Penrose Inverse takes place when e = s = 0.
Properties: a*(a˜*a)=a (a*a˜)*a = a
For non-singular matrix a˜ = aˆ(-1) (or a**(-1) )
The parameters e, s > 0; k < mn provide regularization
(stabilization)