[Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?

[Lennart Fricke]

I read it like that: 
(**T is the transpose)

Let's call M the mass matrix and N the modal mass matrix. Then
X**T*M*X=N. If X (matrix of eigenvectors) is normalized with respect to
M, N is I (unity) so it just mean that X**T*M*X=I. That is what octave
and matlab give you.

For this to be true. x**T*M*x=1 must be true for each column x of X.
Thus if y is the not normalized eigenvector.
a*y**T*M*a*y=1
a**2 * y**T*M*y=1
a**2 = 1/(y**T*M*y)

For me the question, why X diagonalizes M and K at the same time, remains.

Another hint. If the matrizes are hermitian (symmetric if real) you can
use scipy.linalg.eigh, which gives you result with correct
normalization.

Best regards
Lennart