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.