Linear Algebra Done Right · Problem 9D.11

Operators on Real Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · tensor-products

Problem

Suppose

V

and

W

are inner product spaces. Prove that if

S \in \mathcal{L}(V)

and

T \in \mathcal{L}(W)

, then

(S \otimes T)^* = S^* \otimes T^*

, where we are using the notation from the comment after Exercise 9.