Kunze Linear Algebra · Problem 3.7.6

Linear Transformations

Mathematics — Methods · null-space-transpose-differentiation

Problem

Let

n

be a positive integer and let

V

be the space of all polynomial functions over the field of real numbers which have degree at most

n

, i.e., functions of the form

f(x) = c_0 + c_1 x + \cdots + c_n x^n.

Let

D

be the differentiation operator on

V

. Find a basis for the null space of the transpose operator

D^t