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...

In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative)...

In mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables q ( x , y ) = a x 2 + b x y + c y 2 , {\displaystyle q(x...

In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero. Otherwise it...

algebraic number field; the discriminant of a quadratic form; and more generally, the discriminant of a form, of a homogeneous polynomial, or of a projective...

{\displaystyle \varepsilon ^{T}\Lambda \varepsilon } is known as a quadratic form in ε {\displaystyle \varepsilon } . It can be shown that E ⁡ [ ε T Λ...

mathematics, specifically the theory of quadratic forms, an ε-quadratic form is a generalization of quadratic forms to skew-symmetric settings and to *-rings;...

In differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional...

isotropic quadratic form. If Q has the same sign for all non-zero vectors, it is a definite quadratic form or an anisotropic quadratic form. There is...

algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations,...

of the bilinear form and the quadratic form, and it makes sense to speak of the symmetric bilinear form associated with a quadratic form. When char(K) =...

={\begin{cases}q(e_{k})&j=k\\0&j\neq k,\end{cases}}} where q {\displaystyle q} is a quadratic form associated with ⟨ ⋅ , ⋅ ⟩ : {\displaystyle \langle \cdot ,\cdot \rangle...

is a classification of quadratic forms and lattices over the ring of integers. An integral quadratic form is a quadratic form on Zn, or equivalently a...

quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic equation...

In mathematics, a quadratic function of a single variable is a function of the form f ( x ) = a x 2 + b x + c , a ≠ 0 , {\displaystyle f(x)=ax^{2}+bx+c...

that is a root of a quadratic polynomial Quadratic integral, the integral of the reciprocal of a second-degree polynomial Quadratic form (statistics), scalar...

mathematics, a universal quadratic form is a quadratic form over a ring that represents every element of the ring. A non-singular form over a field which represents...

the form bn − (b − 1)n, including the Mersenne primes and the cuban primes as special cases Williams primes, of the form (b − 1)·bn − 1 Of the form ⌊θ3n⌋...

In mathematics, a quadratic equation (from Latin quadratus 'square') is an equation that can be rearranged in standard form as a x 2 + b x + c = 0 , {\displaystyle...

theory, a quadratic field is an algebraic number field of degree two over Q {\displaystyle \mathbf {Q} } , the rational numbers. Every such quadratic field...

theorem is a fundamental result in number theory which states that two quadratic forms over a number field are equivalent if and only if they are equivalent...

form or quadratic form on a vector space over a field, the orthogonal group of the form is the group of invertible linear maps that preserve the form...

set of points whose coordinates satisfy a quadratic equation in two variables which can be written in the form A x 2 + B x y + C y 2 + D x + E y + F = 0...

algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant under a change of basis. Namely, if A {\displaystyle...

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...

Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks...

In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician Cahit Arf (1941)...

_{1}X_{1}+\ldots +\omega _{n}X_{n})}\right]} . One can take the expectation of a quadratic form in the random vector X {\displaystyle \mathbf {X} } as follows:: p.170–171 ...

positive-definite if and only if it is the matrix of a positive-definite quadratic form or Hermitian form. In other words, a matrix is positive-definite if and only...

possible to determine whether there is an integer solution for any quadratic equation of the form x 2 ≡ a mod p {\displaystyle x^{2}\equiv a{\bmod {p}}} for an...