Linear Algebra Done Right · Problem 3C.1

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · matrices-linear-maps

Problem

Suppose

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

. Show that with respect to each choice of bases of

V

and

W

, the matrix of

T

has at least

\dim \operatorname{range} T

nonzero entries.