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quaternion field

См. также в других словарях:

  • 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 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 — /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

  • 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

  • Hurwitz quaternion order — The Hurwitz quaternion order is a specific order in a quaternion algebra over a suitable number field. The order is of particular importance in Riemann surface theory, in connection with surfaces with maximal symmetry, namely the Hurwitz surfaces …   Wikipedia

  • Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… …   Wikipedia

  • Biquaternion — In abstract algebra, the biquaternions are the numbers where w, x, y, and z are complex numbers and the elements of {1, i, j, k} multiply as in the quaternion group. As there are three types of complex number, so there are three types of… …   Wikipedia

  • Polarization — ( Brit. polarisation) is a property of waves that describes the orientation of their oscillations. For transverse waves, it describes the orientation of the oscillations in the plane perpendicular to the wave s direction of travel. Longitudinal… …   Wikipedia

  • William Rowan Hamilton — infobox Scientist name = William Hamilton caption = William Rowan Hamilton birth date = birth date|df=yes|1805|8|4 birth place = Dublin, Ireland death date = death date and age|df=yes|1865|9|2|1805|8|4 death place = Dublin, Ireland residence =… …   Wikipedia

  • List of mathematics articles (Q) — NOTOC Q Q analog Q analysis Q derivative Q difference polynomial Q exponential Q factor Q Pochhammer symbol Q Q plot Q statistic Q systems Q test Q theta function Q Vandermonde identity Q.E.D. QED project QR algorithm QR decomposition Quadratic… …   Wikipedia

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