ABSTRACT

Assuming that n1<n2, show that there exists a constant ?(<1) independent of k such that

for all d lying between ? and 1.

6 Prove Theorem 8.3.4.

(a) Let A, B be defined as in Section 8.6. Show that the roots of det(A-?B)=0 comprise a maximal invariant in the space of (A, B) under Gl(p) transforming

(A, B)? (gAg', gBg'), (b) Show that if r+(N-s)>p, the p×p matrix A+B is positive definite with

probability 1.