Singular Values of Matrix I am working on a problem, and I am trying to show that the singular values of a lower triangular matrix $A$ do not depend on the off-diagonal entries.
I've tried working with $A^TA,$ but I haven't made much progress. Any ideas would be appreciated.

The statement isn't true.  Consider $A=\pmatrix{0 & 0 \\ 1 & 0}$.  If the singular values depended only on the diagonal, they would both be $0$, but they are $0$ and $1$.
