Grothendieck–Witt group

Summary

The Grothendieck–Witt group $GW(F)$ of a field $F$ is the Grothendieck group of nondegenerate quadratic forms over $F$ under orthogonal sum. With the tensor product of forms it is a commutative ring. It keeps both the dimension of a form and its class in the Witt group. The Witt group is the quotient of $GW(F)$ by the multiples of the hyperbolic plane. It is the group $\pi_0$ of Hermitian K-theory, and it appears in motivic homotopy theory.