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!

Homework Help: Proof of Singular Value Decomposition

  1. Sep 26, 2012 #1
    1. The problem statement, all variables and given/known data
    A is arbitrary linear map of the complex vector space s.t. A: V-->V.

    1) Show that there exist unitary matrices s.t A=V*DU where D is diagonal and its entires are non-negative.
    2) Show that part 1 holds if and only if there exist orthonormal bases {u_i} and {v_i} s.t. Au_i=d_i v_i and A*v_i=d_i u_i where u_i is the i-th column of U* and v_i is the i-th column of V*.

    2. Relevant equations

    3. The attempt at a solution
    I was able to successful prove part 1. However, I am really stuck on part 2. I know I need to show both directions since it is an iff proof. So, if I assume these bases exist, I need to be able to derive the SVD.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted