Summary: MAT 310 FALL 09 HOMEWORK 9
Due Wednesday, November 18
1. Let P2[0, 1] be the vector space of real-valued polynomials on [0, 1] with L2 inner product
p, q =
1
0
p(t)q(t)dt.
Define the linear map A : P2[0, 1] P2[0, 1] by
A(a0 + a1x + a2x2
) = a0 - a2x2
.
(a). Show that A is not self-adjoint.
(b) Show that the matrix of A with respect to the "standard" basis {1, x, x2} is
A =


1 0 0
0 0 0
0 0 -1

Source: Anderson, Michael - Department of Mathematics, SUNY at Stony Brook

Collections: Mathematics