In mathematics, a **quadratic form** is a homogeneous polynomial of degree two in a number of variables. For example,

is a quadratic form in the variables *x* and *y*.

Quadratic forms occupy a central place in various branches of mathematics, including number theory, linear algebra, group theory (orthogonal group), differential geometry (Riemannian metric), differential topology (intersection forms of four-manifolds), and Lie theory (the Killing form).

Read more about Quadratic Form: Introduction, History, Real Quadratic Forms, Definitions, Equivalence of Forms, Geometric Meaning, Integral Quadratic Forms

### Other articles related to "quadratic form, forms, quadratic forms, form, quadratic":

**Quadratic Form**s - Universal

**Quadratic Form**s

... An integral

**quadratic form**whose image consists of all the positive integers is sometimes called universal. 4 ≤ d ≤ 14 {1,2,5,d}, 6 ≤ d ≤ 10 There are also

**forms**whose image consists of all but one of the positive integers ... Recently, the 15 and 290 theorems have completely characterized universal integral

**quadratic forms**if all coefficients are integers, then it represents all positive integers if and only if it represents ...

... Cahit Arf, is a knot invariant obtained from a

**quadratic form**associated to a Seifert surface ... a knot, then the homology group H1(F, Z/2Z) has a

**quadratic form**whose value is the number of full twists mod 2 in a neighborhood of an imbedded circle representing an element of the homology group ... The Arf invariant of this

**quadratic form**is the Arf invariant of the knot ...

... dimensional real or complex vector space with a nondegenerate

**quadratic form**Q ... The (real or complex) linear maps preserving Q

**form**the orthogonal group O(V,Q) ... For V real with an indefinite

**quadratic form**, this terminology is not standard the special orthogonal group is usually defined to be a subgroup with two components in this case.) Up to ...

**quadratic Form**- Intuition - Refinements

... An intuitive way to understand an ε-

**quadratic form**is to think of it as a

**quadratic**refinement of its associated ε-symmetric

**form**... the tensor algebra by relations coming from the symmetric

**form**and the

**quadratic form**vw + wv = 2B(v,w) and ... relation follows from the first (as the

**quadratic form**can be recovered from the associated bilinear

**form**), but at 2 this additional refinement is necessary ...

**Quadratic Form**

... 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) for every nonzero vector of V ... According to that sign, the

**quadratic form**is called positive definite or negative definite ... A semidefinite (or semi-definite)

**quadratic form**is defined in the same way, except that "positive" and "negative" are replaced by "not negative" and "not ...

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