Let $V$ be an (infinite dimensional) vector space over the field $\mathbb F (=\mathbb R$ or$ \mathbb C$). If $\alpha$ is the dimension of $V$, for some cardinal number $\alpha$, I want to know, what is the dimension of $V^*$, the algebraic dual of $V$?
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1I’m voting to close this question because it was reposted a few minutes later, and correctly answered over there. – Anne Bauval Oct 19 '23 at 12:48
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$V^*$ is the linear space of all linear maps $r:V\to\mathbb{F}$. That this is indeed a linear space is easy to check. It is an elementary result that the dimensions of $V$ and $V^*$ are equal. To see this, try come up with a basis of $V^*$.
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