You can easily verify that for f:
(1) is linear.
(2) is linear.
(3) and
(4)
So f is a symmetric bilinear form.
Its matrix with respect to the basis B will have entries , which you can find by repeated use of the integration by parts formula.
Hi,
Can anyone help with the following question:
Let Vn be the vector space of of polynomials,
h element of R[x],
deg(f)<= n.
For h,k element of Vn - define:
f(h,k) = integral between 0 and infinity of [ h(x)k(x)(e^-x)] dx
a) Show that f is symmetric bilinear form
b) Let B be the basis {1,X, . . . X^n} of Vn. Find [f] w.r.t B.
You can easily verify that for f:
(1) is linear.
(2) is linear.
(3) and
(4)
So f is a symmetric bilinear form.
Its matrix with respect to the basis B will have entries , which you can find by repeated use of the integration by parts formula.