Kunze Linear Algebra · Problem 3.7.2

Linear Transformations

Mathematics — Methods · transpose-differentiation-operator

Problem

Let

V

be the vector space of all polynomial functions over the field of real numbers. Let

a

and

b

be fixed real numbers and let

f

be the linear functional on

V

defined by

f(p) = \int_a^b p(x)\, dx.

D

is the differentiation operator on

V

, what is

D^t f