Linear Algebra Done Right · Problem 1B.7

Finite-Dimensional Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · vector-space-definition

Problem

Suppose

S

is a nonempty set. Let

V^S

denote the set of functions from

S

V

. Define a natural addition and scalar multiplication on

V^S

, and show that

V^S

is a vector space with these definitions.