Linear Algebra Done Right · Problem 3E.10

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · quotient-spaces

Problem

Suppose

A_1 = v + U_1

and

A_2 = w + U_2

for some

v, w \in V

and some subspaces

U_1, U_2

V

. Prove that the intersection

A_1 \cap A_2

is either a translate of some subspace of

V

or is the empty set.