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Math Help - Don't understand this diagonalizable matrix problem?

  1. #1
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    Don't understand this diagonalizable matrix problem?

    To be honest it has been a while since I've taken Linear Algebra. I'm in my differential equations class and do not recall on how to do this problem.

    Given: The diagonalizable matrix A. Show that the eigenvalues of A^2 are the
    squares of the eigenvalues of A but that A and A^2 have the same eigenvectors.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Don't understand this diagonalizable matrix problem?

    Quote Originally Posted by Reefer View Post
    Given: The diagonalizable matrix A. Show that the eigenvalues of A^2 are the squares of the eigenvalues of A but that A and A^2 have the same eigenvectors.
    Hint If Ax=\lambda x\;(x\neq 0) then, A^2x=A(Ax)=A(\lambda x)=\lambda (Ax)=\lambda \lambda x=\lambda^2x.
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