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Math Help - Proving Eigenvector of transpose matrix

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    Proving Eigenvector of transpose matrix

    If v is an eigenvector of the matrix AA^T (A multiplied by its transpose) with eigenvalue λ, show that A^Tv is an eigenvector of A^TA.

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    Last edited by CaptainBlack; November 15th 2010 at 07:46 AM.
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    MHF Contributor FernandoRevilla's Avatar
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    By hypothesis there exits an scalar \lambda such that (AA^t)v=\lambda v. Then,

    (A^tA)(A^tv)=A^t[(AA^t)v]=A^t(\lambda v)=\lambda(A^tv)

    That is, A^tv is an eigenvector of A^tA.

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