Results 1 to 7 of 7

Math Help - Finding an eigenvector of a symmetric matrix given another eigenvector

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    16

    Finding an eigenvector of a symmetric matrix given another eigenvector

    Hi, I have the problem below and I don't know how to solve it... What property do symmetric matrices have that would allow me to solve it without any calculation? Thanks a lot!

    So here is the problem:

    Find an eigenvector for A (no calculation should be required: note that A is a symmetric matrix).

    A =
    [1, 1]
    [1, -5]

    and the eigenvector given is

    [2]
    [1]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,274
    Thanks
    666
    (2,1) isn't an eigenvector. A(2,1) = (3,-3), which is not in span{(2,1)}. i am confused.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by mbmstudent View Post
    So here is the problem: Find an eigenvector for A (no calculation should be required: note that A is a symmetric matrix).

    A =
    [1, 1]
    [1, -5]

    and the eigenvector given is

    [2]
    [1]

    If the matrix is actually:


    A=\begin{bmatrix}{1}&{\;\;1}\\{1}&{-5}\end{bmatrix}

    then, its eigenvalues are \lambda=-2\pm \sqrt{10} so, perhaps Ramanujan could find the eigenvectors with no calculation.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Mar 2011
    Posts
    40
    Quote Originally Posted by mbmstudent View Post
    Hi, I have the problem below and I don't know how to solve it... What property do symmetric matrices have that would allow me to solve it without any calculation? Thanks a lot!

    So here is the problem:

    Find an eigenvector for A (no calculation should be required: note that A is a symmetric matrix).

    A =
    [1, 1]
    [1, -5]

    and the eigenvector given is

    [2]
    [1]
    For a symmetric matrix it is known that:
    eigenvectors corresponding to different eigenvalues are orthogonal.

    If A has two different eigenvalues and [2, 1] is one of its eigenvectors then [-1, 2] is another one. (because their inner or dot product equals 0)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,274
    Thanks
    666
    Quote Originally Posted by FernandoRevilla View Post
    If the matrix is actually:


    A=\begin{bmatrix}{1}&{\;\;1}\\{1}&{-5}\end{bmatrix}

    then, its eigenvalues are \lambda=-2\pm \sqrt{10} so, perhaps Ramanujan could find the eigenvectors with no calculation.
    no he couldn't...he's dead.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by Deveno View Post
    no he couldn't...he's dead.

    Thanks for the information.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,274
    Thanks
    666
    do i detect a note of sarcasm?

    in any case, the original problem as posed is ill-formed. i urge the original poster to check his input.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove matrix A has same eigenvector as A^2
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 25th 2011, 05:04 AM
  2. Find out eigenvector of this matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 1st 2011, 07:26 PM
  3. Proving Eigenvector of transpose matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 15th 2010, 02:04 AM
  4. Finding the eigenvector
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: June 10th 2009, 10:42 PM
  5. Symmetric matrix eigenvalue and eigenvector
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 7th 2009, 09:44 PM

Search Tags


/mathhelpforum @mathhelpforum