(adsbygoogle = window.adsbygoogle || []).push({}); Is this "theorem" true? Relationship between linear functionals and inner products

Suppose we have a finite dimensional inner product space V over the field F. We can define a map from V to F associated with every vector v as follows:

[tex]\underline{v}:V\rightarrow \mathbb{F}, \ w \mapsto \langle w,v\rangle[/tex]

Clearly this is a linear functional.

My question is whether all linear functionals from V to F are of this form. That is, is it true that for every f in V^{*}, there exists a unique v such that f = v?

I have a felling that it is, but I can't prove it.

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# Is this theorem true? Relationship between linear functionals and inner products

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