Hello

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 eigenvectorv. Then we have A*Av= tv, and taking the inner product withvon both sides implies thatv*A*Av= tv*v.

Butv*A*Av= |Av|2,

How do I finish it off from here?

Cheers