1. Verify that the map I: Mn(C) x M(C) → C given by -> I(M, N) = tr(M¹N) defines an inner product on M. (C). 3. Show that the matrix M = ( is positive definite for all positive integers m -i m such that m 2 2. 4. Suppose HEM, (C) is positive definite. Show that the eigenvalues of H are positive. קוד