Linear Algebra Done Right · Problem 3D.22

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · invertible-linear-maps

Problem

Suppose

T \in \mathcal{L}(V)

and

v_1, \ldots, v_n

is a basis of

V

. Prove that

\mathcal{M}(T, (v_1, \ldots, v_n)) \text{ is invertible} \iff T \text{ is invertible.}