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...atics, a '''linked field''' is a [[Field (algebra)|field]] for which the [[quadratic form]]s attached to [[quaternion algebra]]s have a common property. ...(''x'',''z'').<ref name=Lam>{{cite book | title=Introduction to Quadratic Forms over Fields | volume=67 | series=[[Graduate Studies in Mathematics]] | firs ...

...''E'' is not quadratically closed (as −1 is not a square in ''E'') but the quadratic extension ''E''({{radic|−1}}) is quadratically closed.<ref name=Lam220/> ==Quadratic closure== ...

...it is sometimes more convenient to talk about the square classes which the quadratic form represents. ...tle=Bilinear Algebra: An Introduction to the Algebraic Theory of Quadratic Forms|volume=7|series=Algebra, logic, and applications|first=Kazimierz|last=Szymi ...

...erty as the starting point for a theory of composition of binary quadratic forms Manjul Bhargava went on to define fourteen different composition laws using ==Integer binary quadratic forms== ...

...) for every non-zero vector of {{math|''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 much the same way, except that "always positive" and "al ...

...issn=0092-7872}}</ref> The theorem states that if ''q'' is a nonsingular [[quadratic form]] over a [[Field (mathematics)|field]] ''F'', and <math>\pi(t)\in F[t] ...particular, if <math>W_q(F)</math> denotes the [[Witt group]] of quadratic forms over a field ''F'', then one can construct a group <math>k_n(F)</math> and ...

* {{cite book | title=Introduction to Quadratic Forms over Fields | volume=67 | series=[[Graduate Studies in Mathematics]] | firs [[Category:Quadratic forms]] ...

==Forms== ...>[http://arxiv.org/abs/0805.1658 "Bifurcation Loci of Exponential Maps and Quadratic Polynomials: Local Connectivity, Triviality of Fibers, and Density of Hyper ...

...variant''' of a [[field (mathematics)|field]] describes the structure of [[quadratic form]]s over the field. ...isotropic]], or that every form of dimension at least ''u'' is [[Universal quadratic form|universal]]. ...

.../10.1016/0024-3795(79)90020-X A recurring theorem about pairs of quadratic forms and extensions: a survey]'', Linear Algebra and its Applications, Volume 25 ...

...in 1972 with the dissertation, "Contributions to the theory of semi-simple quadratic algebra"<ref>German title: Beiträge zur Theorie halbeinfacher quadratischer ...ttps://www.sciencedirect.com/science/article/pii/0021869385901358 Reduced forms and reduced Witt rings of higher level]" by Eberhard Becker and Alex Rosenb ...

...lf Hurwitz]]) is the problem of finding multiplicative relations between [[quadratic form]]s which generalise those known to exist between sums of squares in ce ...| author-link=Tsit Yuen Lam | year=2005 | title=Introduction to Quadratic Forms over Fields | series=[[Graduate Studies in Mathematics]] | volume=67 | publ ...

...ternion algebras|linked]]''' if and only if the Albert form is [[isotropic quadratic form|isotropic]], otherwise '''unlinked'''.{{sfn|Lam|2005|p=70}} * The Albert form is [[isotropic quadratic form|anisotropic]]; ...

...math>\varepsilon = (-1)^k</math>. These <math>\varepsilon</math>-quadratic forms define elements in the L-groups <math>L_n (\pi_1 (X))</math>. ...ometry a quadratic formation, which is a kind of automorphism of quadratic forms. Such a thing defines an element in the odd-dimensional L-group <math>L_n ( ...

...r form]]s is another modular form, generalizing the product of two modular forms. ...ions for [[polynomial]]s in [[derivative]]s of modular forms to be modular forms, and {{harvs|txt|last=Cohen|authorlink=Henri Cohen (number theorist)|year=1 ...

| image1 = Quadratic Koch curve type2 iterations.png ...he quadratic type 2 [[Koch curve]], the Minkowski sausage{{efn|name=Type 2|Quadratic Koch curve type 2}} ...

...clidean space]]. It may be described as the set of points for which the [[quadratic form]] for the space applied to the displacement vector from a centre point ...{{math|(''s'', ''t'')}}. The quadratic form is permitted to be [[Definite quadratic form|definite]] (where {{math|1=''s'' = 0}} or {{math|1=''t'' = 0}}), makin ...

...lgorithm to [[Decidability (logic)|decide]] whether a system of diagonal [[quadratic form]]s with integer coefficients represents an integer tuple. Indeed, Büch *[[Paul Vojta|Vojta, Paul]] (1999), ''Diagonal quadratic forms and Hilbert’s tenth problem'', pp.&nbsp;261–274 in ''Hilbert’s tenth proble ...

The ''quadratic map'' of the structure is a map ''P'' from ''V'' to End(''V'') defined in t The quadratic map turns out to be a quadratic polynomial map on ''V''. ...

where ''x'' and ''a'' are integers and ''a'' is a [[quadratic residue]]. * ''a'', an integer which is a quadratic residue <math>\pmod p</math>. ...