Linear Algebra Done Right · Problem 3E.5

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · products-vector-spaces

Problem

For

m

a positive integer, define

V^m

V^m = \underbrace{V \times \cdots \times V}_{m \text{ times}}.

Prove that

V^m

and

\mathcal{L}(\mathbf{F}^m, V)

are isomorphic vector spaces.