Recent content by Laton

Thanks. That sort of makes sense. I guess I have to read up on field automorphisms.

Thanks for the replies. When I wrote "more abstract" I imagined – with hindsight, this may have been a silly idea – "inner product space" being defined for any arbitrary field so that when applied to the complex field, everything would automatically fall into place in such a way that the...

Thanks for all the replies. I see. That makes sense. I see now why it is difficult to define it in more abstract terms. But an inner product is not bilinear, it's sesquilinear. Am I missing something here? A bilinear form may be more general, but I wasn't asking for more general, I was...

There, too, the conjugate symmetry is stated as \left<x,y\right> = \overline{\left<y,x\right>}, but I don't really understand what the conjugate means when we're not talking about complex numbers. That's interesting. So the conjugate can exist for non-complex numbers. Do I have to define it...

Thank you for your reply. I don't think I understand. How is that a metric. This looks like the naturally induced norm of an inner product space. A metric would take two parameters, wouldn't it. I also don't understand why it requires the inner product to take real numbers. The inner product...

An inner product space is often simply described as a vector space with the addition of an inner product, but when it comes to the formal definition, the basefield seems to always be restricted to the fields of real and complex numbers. The Wikipedia article on inner product spaces remarks that...