Results 1 to 2 of 2

Math Help - Diagonalizablilty!! Urgent!! (2)

  1. #1
    Sep 2008

    Diagonalizablilty!! Urgent!! (2)

    Let T be an invertible linear operator on a finite-dimensional vector space V.

    a) Recall that for any eigenvalue λ of T, λ^-1 is an eigenvalue of T^-1. Prove that the eigenspace of T corresponding to λ is the same as the eigenspace of T^-1 corresponding to λ^-1.

    b) Prove that if T is diagonalizable, then T^-1 is diagonalizable
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Apr 2005
    If \lambda is an eigenvalue of A, then Ax= \lambda x for any x in the eigenspace corresponding to \lambda

    Now apply T^{-1} to both sides of that equation.

    (b) is trivial if you think about what "diagonaizable" means.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Urgent!!!help with attempted questions - urgent
    Posted in the Statistics Forum
    Replies: 2
    Last Post: February 28th 2010, 01:29 AM
  2. Matrix Diagonalizablilty
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: December 22nd 2009, 01:16 PM
  3. I need urgent urgent hel with this parabola question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 14th 2008, 05:48 PM
  4. H/W help urgent
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 10th 2008, 01:11 PM
  5. please help...urgent!!
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 23rd 2006, 07:41 AM

Search Tags

/mathhelpforum @mathhelpforum