A First Course in Linear Algebra · Problem MR.M60

Representations — Robert Beezer

Mathematics — Linear Algebra · zero-linear-transformation-matrix-representation

Problem

Suppose

U

and

V

are vector spaces and define a function

Z: U \to V

T(\mathbf{u}) = \mathbf{0}_V

for every

\mathbf{u} \in U

. Then Exercise IVLT.M60 asks you to formulate the theorem:

Z

is invertible if and only if

U = \{\mathbf{0}_U\}

and

V = \{\mathbf{0}_V\}

. What would a matrix representation of

Z

look like in this case? How does Theorem IMR read in this case?