Results 1 to 2 of 2

Math Help - Self-adjoint transformation

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    23

    Self-adjoint transformation

    V is an inner product space over C, and T: V -> V is a self-adjoint transformation. I need to prove that T+iaI is invertible for every real, non-zero a.

    I know that a transformation is not invertible iff it has an eigenvalue 0, but how can i use this?

    Thanks for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,513
    Thanks
    769

    Re: Self-adjoint transformation

    Assume that $T+iaI$ has eigenvalue 0. Derive a contradiction with the fact that eigenvalues of $T$ are real.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: December 5th 2011, 07:33 PM
  2. Self adjoint
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 1st 2011, 10:16 PM
  3. theorem on adjoint of linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 5th 2011, 09:41 PM
  4. Inverse of a self adjoint linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 8th 2010, 02:57 PM
  5. Adjoint of a transformation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 21st 2008, 11:54 AM

Search Tags


/mathhelpforum @mathhelpforum