Exercise 3.E.2

Answers

Proof. Define $T : V_{1} \times \dots \times V_{m} \to V_{j}$ by

T (v_{1}, \dots, v_{m}) = v_{j} .

$T$ is clearly linear and surjective. The Fundamental Theorem of Linear Maps (3.22) now implies that $V_{j}$ is finite-dimensional. □

celiopassos

2017-10-06 00:00