Suppose that M is a nonsingular matrix.
(a) Prove that the implicit iterative scheme M u(n+l) = u(n) is asymptotically stable if and only if all the eigenvalues of M are strictly greater than one in magnitude: |ui) > 1.
(b) Let K be another matrix. Prove that iterative scheme M u(n+1) = K u(n) is asymptotically stable if and only if all the generalized eigenvalues of the matrix pair K, M, as in Exercise 8.4.8, are strictly less than 1 in magnitude: |λ1| < 1.