# Thread: 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.

Please Help >_<

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 $A^tA$.

Regards.

3. What ideas have you had so far?