1. The problem statement, all variables and given/known data If [itex]\lambda_i[/itex] are the eigenvalues of a matrix [itex]A^2[/itex], and [itex]A[/itex] is symmetric, then what can you say about the eigenvalues of A? 2. Relevant equations 3. The attempt at a solution I know how to prove that if [itex]\sqrt(\lambda_i)[/itex] is an eigenvalue of A, then [itex]\lambda_i [/itex] is an eigenvalue of [itex]A^2[/itex]. I don't know how to prove the converse though. Thanks!