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 a mathematical construction based on nonsingular quadratic spaces' isometry classes, employing orthogonal sum and tensor product. The absence of distinction between two spaces differing by a hyperbolic plane requires the explicit definition of an inverse for addition through Grothendieck's work.