Linear Algebra Done Right · Problem 1C.9

Finite-Dimensional Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · subspaces

Problem

A function

f : \mathbf{R} \to \mathbf{R}

is called periodic if there exists a positive number

p

such that

f(x) = f(x + p)

for all

x \in \mathbf{R}

. Is the set of periodic functions from

\mathbf{R}

\mathbf{R}

a subspace of

\mathbf{R}^{\mathbf{R}}

? Explain.