I am trying to get a better intuition for $U$ and $V$ in the SVD. I have read this article which describes $U$ as the normalized projection onto $V$. However, other explanations define $U$ as a rotation matrix that is derived through an eigenvalue decomposition of $AA'$ with $A$ being the to be decomposed matrix.
If it helps, I am looking at neural data and $A$ is an $m\times n$ matrix with $m$ channels of each $n$ samples. Does that mean the components in $U$ are spatial filter and the components in $V$ are temporal filter? I simply cannot reconcile the above two interpretations of $U$ and $V$.
Thank you for your help,
Luca