True or False: (If False then explanation. Thank you.)

11.) If A is positive definite with factorization A = LDL^T , then the diagonal entries of D are the eigenvalues of A.

12.) Suppose Q(x) and R(x) are quadratic forms on R^n . If subject to the constraint llxll =1 themaximum values of Q(x) and R(x) are M_Q and M_R respectively, then subject to the constraint llxll =1 the maximum value of Q(x) + R(x) is M_Q + M_R.

13.) If {u, v} is an orthonormal set in a complex inner product space V, then the set{(u+iv)/sqrt2 , (u-iv)/sqrt2} is also an orthonormal set in V.

14.) The formula = tr(A*B) defines an inner product on the complex vector space C^nn of all n n complex matrices.