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[in Journal: Journal of Algebra and Its Applications] AND [Keyword: Arf Invariant] (1)	29 Mar 2025	Run
[in Journal: Fluctuation and Noise Letters] AND [Keyword: Heart Failure] (1)	29 Mar 2025	Run
[in Journal: Fluctuation and Noise Letters] AND [Keyword: Semiconductor] (2)	29 Mar 2025	Run
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articleNo Access
A CHARACTERIZATION OF NONSINGULAR PAIRS OF QUADRATIC FORMS
- DAVID B. LEEP and
- LAURA MANN SCHUELLER
Journal of Algebra and Its Applications01 Dec 2002
Preview Abstract
Let F, G be a pair of quadratic forms defined over an arbitrary field k. We give a characterization for when every nontrivial zero of F = G = 0 defined over the algebraic closure of k is nonsingular. When chark ≠ 2, this result is well known. When chark = 2, the problem divides into two cases. If n is odd, we use the half-determinant, and if n is even, we use the Arf invariant for this characterization. The characterization depends only on the coefficients of the quadratic forms and operations taking place in the field k.

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