# What is a general scalar and what a (complex conjugate)

I've been reading something about Quantum Mechanics where they introduce the maths slightly more rigorously. They talk about vector spaces and an inner product which yields a scalar. Moreover complex conjugation appears.

Of course I know about complex numbers, but is there a more general framework which defines more generally what a scalar means and also what conjugation (and inner product) means? Maybe some more general algebra which also satisfies some minimum axioms?

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@Gerenuk, sure. The reals are a vector space over the rationals and so are polynomials with rational coefficients and the set $\mathbb Q(\sqrt 2)=\{ a + b \sqrt 2 : a,b \in\mathbb Q\} \subset \mathbb R$. –  lhf Feb 15 '12 at 15:03