Quadratic forms

In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number theory, and algebraic geometry.

homogeneous polynomial of degree two in a number of variables

type of isometry of Euclidean space

mathematical group consisting of transformations of a Euclidean space which preserve distance and a fixed point

algebraic structure generated by a vector space with a quadratic form and a unital associative algebra structure

theorem of matrix algebra of invariance properties under basis transformations

quadratic form that is either greater then 0 except for 0 or less then 0 except for 0

quadratic homogeneous polynomial in two variables

closely-packed repeating pattern of points in 24-dimensional Euclidean space

mathematic formula

vector that is annihilated by a quadratic form

not necessarily associative algebra

two quadratic forms over a number field are equivalent iff they are equivalent locally

theorem on finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form

Function used in local class field theory related to reciprocity laws

theorem

Classify quadratic forms over algebraic number fields

algebra term

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quadratic form q on a vector space which has null vectors; non-zero vectors v for which q(v) = 0

lattice in 8-dimensional space with special properties

integral lattice of determinant 1 or −1