Let $A=U\Lambda V^\top$, $U$, $\Lambda$ and $V$ are respectively left eigenvectors, eigenvalues and right eigenvectors.

$$A^\top A=U\Lambda V^\top V \Lambda U^\top=U\Lambda^2 U^\top$$

So what are the eigenvalues of $A^\top A$ ?

relation between eigenvectors of $A$ and $A^TA$?
Do you think it would be worthwhile to provide hints as to what language to use for the syntax highlighting?

Sometimes I find the highlighting on SQL or VB.NET answers is more distracting than helpful; for example:


Converting MySQL select to PostgreSQL
Retrieving data from a VB.NET arraylist of objects


to pick the two I've been looking at recently.
