# Math Help - Proving Eigenvector of transpose matrix

1. ## 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.

2. 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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