the theory of quadratic forms, an ε-quadratic form is a generalization of quadratic forms to skew-symmetric settings and to *-rings; ε = ±1, accordingly...

In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, 4 x 2...

matrix, then the scalar quantity ε T Λ ε {\displaystyle \varepsilon ^{T}\Lambda \varepsilon } is known as a quadratic form in ε {\displaystyle \varepsilon }...

Chomsky normal form (first described by Noam Chomsky) if all of its production rules are of the form: A → BC,   or A → a,   or S → ε, where A, B, and...

types of quadratic forms. The product zz* is a quadratic form for each of the complex numbers, split-complex numbers, and dual numbers. For z = x + ε y, the...

(σ, ε)-Hermitian form, it follows that for all α in K, σ ( ε ) = ε − 1 {\displaystyle \sigma (\varepsilon )=\varepsilon ^{-1}} σ ( σ ( α ) ) = ε α ε − 1...

{\displaystyle L_{2k}(R)} are defined as the Witt groups of ε-quadratic forms over the ring R with ϵ = ( − 1 ) k {\displaystyle \epsilon =(-1)^{k}} . More precisely...

define quadratic modules first: Let R be a ring with anti-automorphism J, ε ∈ R × {\displaystyle \varepsilon \in R^{\times }} such that r J 2 = ε r ε − 1...

takes a quadratic refinement of the form, which occurs if one has a framed manifold, then the resulting ε-quadratic forms need not be equivalent, being distinguished...

have dimension two, and are known as quadric surfaces. Their quadratic equations have the form A x 2 + B y 2 + C z 2 + D x y + E y z + F x z + G x + H y...