Linear Algebra Done Right · Problem 3C.14

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · transpose

Problem

Suppose

m

and

n

are positive integers. Prove that the function

A \mapsto A^{\mathrm{t}}

is a linear map from

\mathbf{F}^{m,n}

\mathbf{F}^{n,m}