Linear Algebra Done Right · Problem 3E.2

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · products-vector-spaces

Problem

Suppose that V1,…,VmV_1, \ldots, V_m are vector spaces such that V1×⋯×VmV_1 \times \cdots \times V_m is finite-dimensional. Prove that VkV_k is finite-dimensional for each k=1,…,mk = 1, \ldots, m.

Related theory

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