1. The problem statement, all variables and given/known data Let E be the exchange matrix (ones on the anti-diagonal, zeroes elsewhere). Suppose A is symmetric and positive definite. Show that B = EAE is positive definite. 2. Relevant equations 3. The attempt at a solution I've tried showing directly that for any conformable vector h, h'Bh > 0 whenever h'Ah > 0. This looks like a dead end. I suspect the easiest way to get the result is to show all the eigenvalues of B are positive, using the fact that all the eigenvalues of A are positive. However, I don't know how to show this.