matrix computation

Dear Sir:

I try to learn to use the linear algebra in maple.
I try to compute the following matrices.

restart;
assume(a>0,b>0,c>0);
with(LinearAlgebra):
M:=Matrix([[a, 0],[0, b]]);
K:=Matrix([[c,-c],[-c,c]]);
V:=Eigenvectors(K,M);
X:=V[2];
Multiply(Multiply(X^%T,M),X);

I expect that the final result should be the indentity
matrix. However, it does not produce what I expect.
Please give me some advice to get the identity matrix.

Thank you.

Comments

Mistaken identity?

Why do you expect to obtain an identity matrix?

J. Tarr

identity

In general, it is the orthogonality condition of
eigenvalue problems. That is why I expect an identity
matrix.

Thanks,

maybe not in that case?

Hi,

I have no time to prove the identity you mentioned here, but even if it were true, it might not work in the case as the matrix K is a singular one.

I am eager to see the proof first of all.

The general eigenvector

The general eigenvector problem K.x=lambda.M.x gives the same set of eigen values and vectors as the simple eigenvalue problem M^(-1).K.x=lambda.x . However, since M^(-1).K is not symmetric, the eigenvectors are not orthogonal.

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