Linear Algebra Done Right · Problem 3E.4

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · products-vector-spaces

Problem

Suppose

W_1, \ldots, W_m

are vector spaces. Prove that

\mathcal{L}(V, W_1 \times \cdots \times W_m)

and

\mathcal{L}(V, W_1) \times \cdots \times \mathcal{L}(V, W_m)

are isomorphic vector spaces.