Definition talk:Semi-Inner Product

I have a problem with the definition section of this page:

Given the following line:


 * Let $V$ be a vector space over a subfield $\mathbb F$ of $\C$.

and the result Complex Numbers form Vector Space. We have that our vector space may be the complex numbers.

So the semi-inner product may be the mapping: $\left \langle {\cdot, \cdot} \right \rangle : V \times V \to \mathbb C$

In other words we feed two vectors in and get a complex number out.

But then condition $(4)$ says:


 * $(4): \quad \left \langle {x, x} \right \rangle \ge 0$

Which doesn't make sense based on Complex Numbers Can Not be Ordered.

Again, this stuff is way over my head. But it's an important definition and I felt like I should say something. --Jshflynn (talk) 10:07, 28 September 2012 (UTC)


 * Yes, sorry about that. I was trying to generalise stuff without contemplation at the time. The whole functional analysis section (of which this is about the first baby step) is due for reworking after more basic fields have been treated (I stopped mainly because there was a lack of internal references I could use; as my book is quite advanced, it is almost impossible to provide the desired standard of rigour at the moment). For now, I have added a "questionable" mark to indicate that the page may not be correct. --Lord_Farin (talk) 13:49, 28 September 2012 (UTC)