Results 1 to 2 of 2

Math Help - Prove matrix A has same eigenvector as A^2

  1. #1
    Senior Member
    Joined
    Apr 2010
    Posts
    487

    Prove matrix A has same eigenvector as A^2

    The question
    If A is a matrix with eigenvector v and corresponding eigenvalue \lambda prove that v is also an eigenvector of A^2 and find the corresponding eigenvalue.

    I'm not sure how to attempt this. Any hints?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,386
    Thanks
    752

    Re: Prove matrix A has same eigenvector as A^2

    Av = λv.

    so A^2(v) = A(λv) = λ(Av) = .....?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find out eigenvector of this matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 1st 2011, 07:26 PM
  2. Replies: 6
    Last Post: April 11th 2011, 12:18 PM
  3. Proving Eigenvector of transpose matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 15th 2010, 02:04 AM
  4. Replies: 1
    Last Post: April 1st 2010, 08:34 AM
  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