# Linear Transformations 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.

$\blacksquare$