I have a positive semi definite real matrix $ A $. I know I can find a real matrix B such that $ A = BB^T $. It is clear that I can add a zero column to $B$ and $ A = BB^T $ still holds for my new matrix $B$. But can I find a different square matrix $B$ such that $ A = BB^T $ or is it that this factorization is unique if I require that $B$ is square ?
Thanks!