Linear Algebra Done Right · Problem 7E.6

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · singular-value-decomposition

Problem

Find the singular values of the differentiation operator

D \in \mathcal{L}(\mathcal{P}_2(\mathbf{R}))

defined by

Dp = p'

, where the inner product on

\mathcal{P}_2(\mathbf{R})

is as in Example 6.34.