Let V {\displaystyle {}V} and W {\displaystyle {}W} be vector spaces over a field K {\displaystyle {}K} , with a basis v 1 , … , v n {\displaystyle {}v_{1},\ldots ,v_{n}} of V {\displaystyle {}V} , and a basis w 1 , … , w m {\displaystyle {}w_{1},\ldots ,w_{m}} of W {\displaystyle {}W} . Show that
is a basis of the space of homomorphisms Hom K ( V , W ) {\displaystyle {}\operatorname {Hom} _{K}{\left(V,W\right)}} .
and 
be
vector spaces
over a
field
, with a
basis
of , and a basis 
of . Show that
.
