Results 1 to 2 of 2

Math Help - Eigenvectors

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    14

    Exclamation Eigenvectors

    Suppose A is a symmetric N N matrix with eigenvectors vi, i = 1, 2, 3 N with
    corresponding eigenvalues λi, i = 1, 2,3 N.
    Pick any two distinct eigenvalues (assuming such a pair exists). Let's call them λ1 and λ 2 and their corresponding eigenvectors v1 and v2.
    (a) Write down the matrix equations that show that v1 and v2 are eigenvectors of A.
    (b) Compute the transpose of the equation satisfied by v2.
    (c) Multiply, from the right, the result of part (b) by v1.
    (d) Use the assumptions that A is symmetric and λ1≠ λ 2 to deduce a value for vT
    2 v1.
    (e) What important property can you deduce from your result in part (d)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21

    Re: Eigenvectors

    Quote Originally Posted by bakchormee View Post
    Suppose A is a symmetric N N matrix with eigenvectors vi, i = 1, 2, 3 N with
    corresponding eigenvalues λi, i = 1, 2,3 N.
    Pick any two distinct eigenvalues (assuming such a pair exists). Let's call them λ1 and λ 2 and their corresponding eigenvectors v1 and v2.
    (a) Write down the matrix equations that show that v1 and v2 are eigenvectors of A.
    (b) Compute the transpose of the equation satisfied by v2.
    (c) Multiply, from the right, the result of part (b) by v1.
    (d) Use the assumptions that A is symmetric and λ1≠ λ 2 to deduce a value for vT
    2 v1.
    (e) What important property can you deduce from your result in part (d)?
    Let's see some work mayne.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Eigenvectors
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: September 26th 2010, 08:26 AM
  2. eigenvectors
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 16th 2009, 05:07 AM
  3. Eigenvectors
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 10th 2009, 06:10 AM
  4. eigenvectors
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: May 6th 2008, 03:07 PM
  5. Eigenvectors
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 21st 2008, 11:53 AM

Search Tags


/mathhelpforum @mathhelpforum