The Grothendieck-Witt ring GW is a related construction generated by isometry classes of nonsingular quadratic spaces with addition given by orthogonal sum and multiplication given by tensor product. Since two spaces that differ by a hyperbolic plane are not identified in GW, the inverse for the addition needs to be introduced formally through the construction that was discovered by Grothendieck (see Grothendieck group).
The Grothendieck-Witt ring GW is derived from nonsingular quadratic spaces' isometry classes, employing orthogonal sum as addition and tensor product as multiplication. However, since hyperbolic planes do not distinguish two spaces in GW, an inverse for the addition must be explicitly defined through Grothendieck's construction.