3.52 Let A be an mxm positive definite matrix and B be an mxm nonnegative definite matrix. 3.51 Show mal Il A IS à nonnegative definite matrix and a 0 for some z, then ai,-G3 = 0 for all j definite matrix. (a) Use the spectral decomposition of A to show that 3.52 Let A be an m x m positive definite matrix and B be an m × m nonnegative with equality if and only if B (0). (b) Show that if B is also positive definite and A - B is nonnegative definite, then |Al 2 IB| with equality if and only if A - B. ss suppose that 'A is an m x m symmetric matrix with eigenvalues λι, . . . Am 3.51 Show mal Il A IS à nonnegative definite matrix and a 0 for some z, then ai,-G3 = 0 for all j definite matrix. (a) Use the spectral decomposition of A to show that 3.52 Let A be an m x m positive definite matrix and B be an m × m nonnegative with equality if and only if B (0). (b) Show that if B is also positive definite and A - B is nonnegative definite, then |Al 2 IB| with equality if and only if A - B. ss suppose that 'A is an m x m symmetric matrix with eigenvalues λι, . . . Am