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: 6 orthonormal subspace question

  1. Oct 28, 2011 #1
    6)there is normal T in unitarian final space.
    [tex]v\neq0,v\in V[/tex] prove that if [tex]\{sp(v)\}^{\perp}[/tex] is T variant then
    v is eigenvector of T
    ?
    hint:prove that [tex]T*(v)[/tex] is orthogonal to [tex]\{sp(v)\}^{\perp}[/tex]
    what i have done:
    suppose [tex]u\in\{sp(v)\}^{\perp}[/tex]
    we take the definition of [tex]T*[/tex]
    (Tu,v)=(u,T*v)
    (Tu,v)=0 because [tex]\{sp(v)\}^{\perp}[/tex] is T variant so T*v is orthogonal
    to u.
    i know also
    V=[tex]\{sp(v)\}^{\perp}\oplus\{sp(v)\}[/tex]
    what to do next ,how to prove the actual question?
     
  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



Loading...