Set of Linear Transformations is Isomorphic to Matrix Space/Corollary

Corollary to Linear Transformations Isomorphic to Matrix Space
Let $R$ be a commutative ring with unity.

Let $M: \struct {\map {\mathcal L_R} G, +, \circ} \to \struct {\map {\mathcal M_R} n, +, \times}$ be defined as:


 * $\forall u \in \map {\mathcal L_R} G: \map M u = \sqbrk {u; \sequence {a_n} }$

Then $M$ is an isomorphism.

Proof
Follows directly from Linear Transformations Isomorphic to Matrix Space.