Results 1 to 3 of 3

Math Help - Question on orthonormal basis of eigenvectors for a normal operator T

  1. #1
    Newbie
    Joined
    Apr 2013
    From
    Canada
    Posts
    7

    Question on orthonormal basis of eigenvectors for a normal operator T

    Hello,
    any help on this question is greatly appreciated.
    "For each linear operator T on an inner product space V, determine wheter T is normal, self-adjoint, or neither. If possible, produce an orthonormal basis of eigenvectors of T for V and list the corresponding eigenvalues.

    (c) V=C2 and T is defined by T(a,b) = (2a + ib , a + 2b)"

    So, I know T is not self-adjoint and that it is normal since TT*=T*T and since it's over C2, there has to be an orthonormal basis of eigenvectors, but I can't find them.
    Using the standard basis B, A = [T]B = [2 i]
    [1 2]

    and det(A-tI) = t^2 - 4t + 4 - i
    If I use the quadratic formula I get 2 +- (1+i)/sqrt(2)
    Should I pursue this further or am I doing something wrong. I am unable to find the eigenvectors.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: Question on orthonormal basis of eigenvectors for a normal operator T

    Hey Migno.

    Can you show us your row reduction operations for both eigen-vectors? (The approach you used to get the eigen-values is OK).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2013
    From
    Canada
    Posts
    7

    Re: Question on orthonormal basis of eigenvectors for a normal operator T

    I see, it just looked funny haha. I got it now, thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Orthonormal Set of Eigenvectors of A
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: December 11th 2011, 12:43 AM
  2. Replies: 1
    Last Post: November 24th 2009, 06:57 PM
  3. Orthonormal Basis question
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 13th 2009, 10:31 AM
  4. orthonormal basis question
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 24th 2008, 11:28 PM
  5. Orthonormal basis
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 10th 2008, 10:52 AM

Search Tags


/mathhelpforum @mathhelpforum