Linear Algebra Done Right · Problem 5E.8

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · commuting-operators

Problem

Suppose

m = 3

in Example 5.72 and

D_x, D_y

are the commuting partial differentiation operators on

\mathcal{P}_3(\mathbf{R}^2)

from that example. Find a basis of

\mathcal{P}_3(\mathbf{R}^2)

with respect to which

D_x

and

D_y

each have an upper-triangular matrix.