# Witt group of real number

Question: How can one compute the Witt group, for example for real numbers? According to Wikipedia it is Z, but how? Any reference would be appreciated.

• That's basically Sylvester's Law of Inertia. – Lord Shark the Unknown Sep 29 '18 at 17:08

One way to think Witt group is find square classes in field . It is easy to see that there is one - one correspondence between quadratic form and bilinear form. Idea of finding Witt group is to define some invariant map such as dimension or signature etc. In case of real number we define homomorphism from Witt group of $$\mathbb{R}$$ to $$\mathbb{Z}$$ by using signature map. Where signature is just differnce between number of positive definite quadratic form and negative definite quadratic forms.