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: ST and TS have the same eigenvals

  1. Nov 2, 2006 #1

    I need to prove that for S,T linear operators on V. ST and TS have the same eigenvalues. I've gotten as far as (say g is the eigenvalue and u is a nonzero vector): STu=gu so TS(Tu)=g(Tu). So TS has eigenvalue g corresponding to eigenvector Tu. But I don't know how to guarantee that Tu is nonzero. (Or how to resolve the possibility that it is zero)

    Thanks for any help.
  2. jcsd
  3. Nov 2, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If Tu is zero, what's STu?
  4. Nov 2, 2006 #3
    If Tu=0

    STu=0=gu, but u is nonzero, so g=0?

    So does zero as an eigenvalue become a special case? Then would I do the nonzero eigenvalue case separately?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook