Results 1 to 2 of 2

Math Help - How do I orthogonally diagonalize a matrix?

  1. #1
    Newbie
    Joined
    Jul 2009
    Posts
    1

    How do I orthogonally diagonalize a matrix?

    I'm given a matrix


    A = -3 0 -4
    0 5 0
    -4 0 3

    I have to orthogonally diagonalize the matrix and give the orthogonal matrix P and the diagonal matrix D. I have no idea how to do this.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,048
    Thanks
    1684
    Quote Originally Posted by lovestoskate View Post
    I'm given a matrix


    A = -3 0 -4
    0 5 0
    -4 0 3

    I have to orthogonally diagonalize the matrix and give the orthogonal matrix P and the diagonal matrix D. I have no idea how to do this.
    This is a "symmetric" matrix and so must have 3 independent eigenvectors. In fact, eigenvectors corresponding to different eigenvalues must be orthogonal.

    So do this: find the eigenvalues and the corresponding eigenvectors. If there is a "double" or "triple" eigenvalue, you can find vectors in that eigenspace that are orthogonal. Divide each eigenvector by its length to get unit vectors.

    Form matrix Q using those vectors as columns. Then Q and Q^{-1} are orthogonal matrices and Q^{-1}PQ is diagonal.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding diagonalize matrix
    Posted in the Advanced Algebra Forum
    Replies: 18
    Last Post: November 6th 2010, 10:07 AM
  2. Diagonalize unitary matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 9th 2009, 08:08 PM
  3. Orthogonally diagonalizable
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 8th 2009, 04:30 AM
  4. Orthogonally diagonalize the matrix
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: April 22nd 2009, 02:39 AM
  5. Orthogonally diagonalize the symmetric matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 15th 2008, 07:26 AM

Search Tags


/mathhelpforum @mathhelpforum