User talk:2001:67C:10EC:5746:8000:0:0:166

Definition of inner product is wrong
Hi, the definition on the inner product page is wrong.

The third point, namely, that the inner product needs to be positive definite is not true. I checked the reference that was cited and I think the error occurred because the text was not read properly.

In his book, he does indeed give a "positive definity"-condition for the inner product but that is just because he says that for the purposes of his book he will only focus on positive definite inner products!! In his definition for the inner product he also does NOT use the positivity condition but only introduces it later on.

However, in general, an inner product does not need to be positive definite! This is very important and including a condition that it has to be positive definite in the definition of an inner product is not correct!

If you want another source, you can use "Manifolds, Tensors and Forms" from Paul Renteln, pages 14 and 15.

I hope this helps fix this mistake. Thank you!

P.S. For now, I added a small note under the definition on the page so that people are made aware of this. However, I'm not an expert on formatting and stuff, so I hope someone better equipped than I will make the appropriate changes in an esthetically pleasing manner.