Linear Transformations Isomorphic to Matrix Space/Corollary

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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.

$\blacksquare$

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