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: Similarity and change of basis

  1. Jul 21, 2007 #1
    1. The problem statement, all variables and given/known data

    Consider the 2-dimensional complex vector space V of functions spanned by sin x and cos x. For a fixed real number α, define a linear operator T ≡ Tα on V by putting T(f(x)) = f(x + α). Find the matrices [T]B and [T]E of T relative to the bases B = {cos x, sin x} and E = {cos x + i sin x, cos x − i sin x}. Find an invertible matrix P implementing the similarity between [T ]B and [T]E :

    [tex][T]_B = P[T]_EP^{-1}[/tex]

    2. Relevant equations

    3. The attempt at a solution

    I found T_B and T_E and I think I'm probably right because their tr and det are equal. Sorry if I don't show all that work because it is long. My problem is to get P. I am not sure how to get this. Thanks for any suggestions.
  2. jcsd
  3. Jul 21, 2007 #2


    User Avatar
    Homework Helper

    Well, what do you know about transformation matrices between different bases?
  4. Jul 21, 2007 #3
    OK. Got it now.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook