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I've been trying to find the most general definition of an inner product space.

Every definition I've found is either to $\mathbb{R}$ or to $\mathbb{C}$. Is it possible to define an inner product to an arbitrary field? In other words, is there a more general way of formulating the conjugate symmetry property?

EDIT: It would have to be an ordered field to have positive definiteness make sense, I guess.

Syd Kerckhove
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    Essentially the same question was asked on MO: http://mathoverflow.net/questions/6701/definition-of-inner-product-for-vector-spaces-over-arbitrary-fields – Travis Willse Oct 16 '15 at 08:22

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