Dimension of Algebraic Dual
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Split off Dimension of Double Dual
Split off Dimension of Double Dual
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Theorem
Let $G$ be an $n$-dimensional $R$-module.
Let $G^*$ be the algebraic dual of $G$.
Let $G^{**}$ be the algebraic dual of $G^*$.
Then $G^*$ and $G^{**}$ are also $n$-dimensional.
Proof
Follows directly from Product of Linear Transformations.
$\blacksquare$
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): $\S 28$