Linear Algebra Done Right · Problem 3D.7

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · invertible-linear-maps

Problem

Suppose that

V

is finite-dimensional and

S, T \in \mathcal{L}(V, W)

. Prove that

\operatorname{range} S = \operatorname{range} T

if and only if there exists an invertible

E \in \mathcal{L}(V)

such that

S = TE