quaternion algebra

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• Quaternion algebra — In mathematics, a quaternion algebra over a field, F , is a particular kind of central simple algebra, A , over F , namely such an algebra that has dimension 4, and therefore becomes the 2 times;2 matrix algebra over some field extension of F ,… …   Wikipedia

• Quaternion — Quaternions, in mathematics, are a non commutative extension of complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three dimensional space. They find uses in both… …   Wikipedia

• Quaternion — ℍ Gedenktafel an der Broom Bridge in Dublin, wo William Rowan Hamilton die Multiplikationsregeln im Oktober 1843 spontan in den Stein ritzte. Die Quaternio …   Deutsch Wikipedia

• Quaternion group — In group theory, the quaternion group is a non abelian group of order 8. It is often denoted by Q and written in multiplicative form, with the following 8 elements : Q = {1, −1, i , − i , j , − j , k , − k }Here 1 is the identity element, (−1)2 …   Wikipedia

• Algebra over a field — This article is about a particular kind of vector space. For other uses of the term algebra , see algebra (disambiguation). In mathematics, an algebra over a field is a vector space equipped with a bilinear vector product. That is to say, it is… …   Wikipedia

• Quaternion Society (1899 - 1913) — A scientific society, the Quaternion Society was an “International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics”. At its peak it consisted of about 60 mathematicians spread throughout the academic world… …   Wikipedia

• Algebra — This article is about the branch of mathematics. For other uses, see Algebra (disambiguation). Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from… …   Wikipedia

• algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… …   Universalium

• *-algebra — * ring= In mathematics, a * ring is an associative ring with a map * : A rarr; A which is an antiautomorphism, and an involution.More precisely, * is required to satisfy the following properties: * (x + y)^* = x^* + y^* * (x y)^* = y^* x^* * 1^* …   Wikipedia

• algebra, modern — ▪ mathematics Introduction also called  abstract algebra        branch of mathematics concerned with the general algebraic structure of various sets (such as real numbers (real number), complex numbers (complex number), matrices (matrix), and… …   Universalium

• Dual quaternion — The set of dual quaternions is an algebra that can be used to represent spatial rigid body displacements.[1] A dual quaternion is an ordered pair of quaternions  = (A, B) and therefore is constructed from eight real parameters. Because rigid… …   Wikipedia