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quaternion group

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  • 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

  • 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 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

  • Quaternion — Qua*ter ni*on, n. [L. quaternio, fr. quaterni four each. See {Quaternary}.] 1. The number four. [Poetic] [1913 Webster] 2. A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances,… …   The Collaborative International Dictionary of English

  • 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-Kähler manifold — In differential geometry, a quaternion Kähler manifold (or quaternionic Kähler manifold) is a Riemannian manifold whose Riemannian holonomy group is a subgroup of Sp( n )·Sp(1). Another, more explicit, definition, uses a 3 dimensional subbundle H …   Wikipedia

  • Quaternion-Kähler symmetric space — In differential geometry, a quaternion Kähler symmetric space or Wolf space is a quaternion Kähler manifold which, as a Riemannian manifold, is a Riemannian symmetric space. Any quaternion Kähler symmetric space with positive Ricci curvature is… …   Wikipedia

  • Group action — This article is about the mathematical concept. For the sociology term, see group action (sociology). Given an equilateral triangle, the counterclockwise rotation by 120° around the center of the triangle acts on the set of vertices of the… …   Wikipedia

  • Mathieu group — Group theory Group theory …   Wikipedia

  • quaternion — /kweuh terr nee euhn/, n. 1. a group or set of four persons or things. 2. Bookbinding. four gathered sheets folded in two for binding together. 3. Math. a. an expression of the form a + bi + cj + dk, where a, b, c, and d are real numbers; i2 = j2 …   Universalium

  • quaternion — noun /kwɒˈtɜːniɒn/ a) A group or set of four people or things.<ref name= COED etym sense /> 1885, Alexander Roberts, James Donaldson (original translators and editors), Arthur Cleveland Coxe (editor of American edition, unauthorized; author …   Wiktionary

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