I already know the concept of SVD applyed on an mxn matrix. Eigen vectors can't exist for a non-square matrix, but singular-vectors can. My question is: does SVD on a square matrix relate to eigendecomposition in a way?
SVD:
$M=UEV^*$, where M is mxn, $U$ is mxm, $E$ is mxn and $V^*$ is nxn
Now if M is mxm, then: $U$ is mxm, $E$ is mxm and $V^*$ is also mxm, which resembles a lot the eigendecomposition (case where U=V).