Classifying nonsingular quadratic forms of rank three

Citations of this article
Mendeley users who have this article in their library.
Get full text


The determinant on 2 by 2 matrices of trace zero gives a quadratic form. Linear algebra shows that its orthogonal group is the matrix algebra automorphisms together with scalars of square 1. As this holds over all commutative rings, descent theory can be applied to it to get a quick classification of all nonsingular quadratic forms of rank 3. Further descent arguments show how this classification yields the Witt invariant and discriminant. © 1990.




Waterhouse, W. C. (1990). Classifying nonsingular quadratic forms of rank three. Linear Algebra and Its Applications, 142(C), 55–61.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free