88 N.M. Katz: Then the matrix of f(-a, -b, -c) on N is /P(O) Q(O) P(1) Q(I!. (188.8.131.52) t @(2) ." ." ." ..." '. It's proper values are thus its diagonal terms. If a = b, then all but one of these diagonal terms is non-zero, and hence zero is a proper value of multiplicity one, which implies that the kernel of g(- a, - b, - c) in N is one dimensional. Thus we may assume a +b, and that a< b, since the problem is symmetric in a and b. As a + b, the matrix (184.108.40.206) has precisely two diagonal terms which vanish, namely P(a) and P(v). The subspace N(<b) of N consisting of polynomials of degree <b is stable under (, and f is invertible on
This is the end of the preview. Sign up
access the rest of the document.