Linear Algebra Done Right · Problem 3E.9

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · quotient-spaces

Problem

Prove that a nonempty subset

A

V

is a translate of some subspace of

V

if and only if

\lambda v + (1 - \lambda)w \in A

for all

v, w \in A

and all

\lambda \in \mathbf{F}