how do i prove that all the eigenvalues of the product A*A (where A* is the conjugate transpose matrix of A) are real non negative numbers. note A is not necessarily a square matrix ?
Letting t be an eueigenval of A*A, with eigenvector v. Then we have A*Av = tv, and taking the inner product with v on both sides implies that v*A*Av = tv*v.
But v*A*Av = |Av|2,
How do I finish it off from here?