1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Eigenvector eigenvalue proof problem

  1. Jan 6, 2012 #1
    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!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?