Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hermitian General Eigenvalue Problem

  1. Jul 28, 2013 #1
    Hello~ I've been trying to understand where this orthogonality comes from but I haven't determined a solution. I was wondering if someone could shed some light on this problem. Basically, given
    {\bf Ax}_n=\lambda_n{\bf Bx}_n \\
    {\bf v}=\sum_nc_n{\bf x}_n

    when is the following true:
    c_n=\frac{{\bf x}_n^T{\bf Bv}}{{\bf x}_n^T{\bf Bx}_n}

    and why. In my particular problem, I believe [itex]{\bf A}[/itex] is singular and hermitian. I've also read that [itex]{\bf B}[/itex] may have to be positive definite for this orthogonality to occur. I'd be happy if both singular and non-singular cases are addressed.

    Thanks :)

    The orthogonality is
    \frac{{\bf x}_i^T{\bf Bx}_j}{{\bf x}_i^T{\bf Bx}_i}=\delta_{i,j}
    Last edited: Jul 28, 2013
  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?
Draft saved Draft deleted