I get that in the case of a real $n\times n$ matrix, $M$, in the SVD of $M = USV^T$, $U$ represents rotation and/or reflection in the input basis, $S$, the set of singular values denotes scaling and $V$ represents rotation and/or reflection in the output basis.
How to separate rotation and reflection in both input basis and output basis? And specifically, how does this work when the original matrix is complex?
Thanks