Linear Algebra Done Right · Problem 3D.15

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · invertible-linear-maps

Problem

Suppose

T \in \mathcal{L}(V)

and

v_1, \ldots, v_m

is a list in

V

such that

Tv_1, \ldots, Tv_m

spans

V

. Prove that

v_1, \ldots, v_m

spans

V