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.
$\blacksquare$
If you are fairly certain that there are none, please remove {{proofread}} from the code.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): $\S 29$: Theorem $29.2$