# Eigenvector eigenvalue proof problem

1. Jan 6, 2012

### iqjump123

1. The problem statement, all variables and given/known data

Let A and B be symmetric matrices and X is a vector in the eigenvalue problem
AX-λBX=0

a) Show that the eigenvectors are orthogonal relative to A and B.

b) If the eigenvectors are orthonormal relative to B , determine C such that (C-λI)X=0, where C is a diagonal matrix.

2. Relevant equations
Orthogonal eigenvectors: transpose(Xi)*A*(Xj)=0 and transpose(Xi)*B*Xj=0

Orthonormal eigenvectors: transpose(Xi)*B*Xj=I
3. The attempt at a solution

I am able to extract out eigenvalues and eigenvectors from matrices when used to solve systems of equations, etc, but I don't know how I can use that to prove the theorem above. Should I try a set of random 2x2 numerical matrix and try to get values? An explanation of the problem and a basic starting step to complete this problem will be helpful.

thanks!