Results 1 to 2 of 2

Math Help - Complex eigenvectors

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    10

    Complex eigenvectors

    Hi!

    A complex 2x2 matrix is given as

    A =
    a b
    c d
    
    where a, b, c and d are complex numbers.

    Find the eigenvectors of U when a = 0, b = i, c = -i and d = 0, and normalize
    them to unity.

    I think I've found the eigenvalues to be 1 and -1. (If that is right.)
    But I have problem finding the eigenvectors. I know how you should do it, and know the equation and so on, but I don't get any results. I need someone to show me how you get the answer.

    Looking forward for help!

    Best regards!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: Complex eigenvectors

    Quote Originally Posted by expresstrain View Post
    I think I've found the eigenvalues to be 1 and -1. (If that is right.)
    Right.

    But I have problem finding the eigenvectors. I know how you should do it, and know the equation and so on, but I don't get any results. I need someone to show me how you get the answer.
    \ker (A-I) \equiv\begin{Bmatrix} -x_1+ix_2=0\\-ix_1-x_2=0\end{matrix} ... a basis is B_1=\{(i,1)\} . Now, normalize it.

    \ker (A+I) \equiv\ldots
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with Eigenvectors
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 12th 2011, 02:22 PM
  2. Complex Eigenvectors
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: December 25th 2010, 12:12 AM
  3. Eigenvectors
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: September 26th 2010, 09:26 AM
  4. Complex eigenvalues/eigenvectors
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 4th 2010, 07:23 PM
  5. Eigenvectors
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 10th 2009, 07:10 AM

Search Tags


/mathhelpforum @mathhelpforum