Search results
Jump to navigation
Jump to search
Page title matches
- ...subalgebra of the dual quaternions which will later be called the ''planar quaternions''. The '''planar quaternions''' make up a four-dimensional [[Algebra over a field|algebra]] over the [[r ...10 KB (1,505 words) - 21:27, 19 January 2025
Page text matches
- * [[Vector space]] <!-- Doesn't mention the quaternions, but should!--> * [[General linear group]] <!-- Doesn't mention the quaternions, but should!--> ...2 KB (331 words) - 04:52, 8 November 2024
- {{short description|Specific set of Hamiltonian quaternions with the same symmetry as the 600-cell}} ...cosian [[Group (mathematics)|group]]''': a [[multiplicative group]] of 120 quaternions, positioned at the vertices of a 600-cell of unit radius. This group is [[g ...4 KB (559 words) - 01:05, 19 January 2025
- ...hematical-society/volume-50/issue-4/The-fundamental-theorem-of-algebra-for-quaternions/bams/1183505735.full|journal=[[Bulletin of the American Mathematical Societ ...al=Acad. Sinica Science Record|volume=3|pages=29–33}}</ref> Different from quaternions, however, the monic and non-monic octonionic polynomials do not have always ...3 KB (374 words) - 08:16, 15 August 2023
- ...iption|Event commemorating the Irish mathematician Hamilton's discovery of quaternions}} These are the basic relations which define the quaternions. The original inscription by Hamilton is no longer there, but a plaque ere ...4 KB (593 words) - 04:58, 26 January 2023
- ...subalgebra of the dual quaternions which will later be called the ''planar quaternions''. The '''planar quaternions''' make up a four-dimensional [[Algebra over a field|algebra]] over the [[r ...10 KB (1,505 words) - 21:27, 19 January 2025
- The '''commutative quaternion model''', also known as the '''(2,2)-model of quaternions''', is an alternative quaternion algebra that ensures commutative multiplic Quaternions were introduced by '''Sir William Rowan Hamilton''' in 1843 as an extension ...6 KB (783 words) - 20:04, 19 February 2025
- .../3/4/3/6/34363841/blaschke_-_kinematics_and_quaternions.pdf Kinematics and Quaternions], page 47, translated by D. H. Delphenich</ref> Kotelnikov began instructin ==Dual quaternions== ...6 KB (756 words) - 20:16, 6 November 2024
- ...ersor]]s with a fixed axis ''r'':<ref name=GL>[[Georges Lemaître]] (1948) "Quaternions et espace elliptique", ''Acta'' [[Pontifical Academy of Sciences]] 12:57&nd [[Category:Quaternions]] ...5 KB (672 words) - 22:56, 24 May 2024
- ...n part to the lack of a suitable calculus of [[holomorphic function]]s for quaternions. The most succinct definition uses the language of [[G-structure on a manif ...nhance this group with the group <math>\mathbb{H}^\times</math> of nonzero quaternions acting by scalar multiplication on <math>\mathbb{H}^n</math> ''from the rig ...10 KB (1,526 words) - 00:15, 14 September 2024
- The quaternions form a [[noncommutative]] [[ring (algebra)|ring]], and therefore [[Matrix a ...r (square) quaternionic matrices so that the values of the determinant are quaternions.<ref>{{cite journal |author=Helmer Aslaksen |title=Quaternionic determinant ...4 KB (645 words) - 08:18, 17 December 2023
- ...uthor of the book ''Conformal Geometry of Surfaces in <math>S^4</math> and Quaternions'' (Springer, 2002), developing the theory of [[quaternionic analysis]].{{r| ...me=cgs>Reviews of ''Conformal Geometry of Surfaces in <math>S^4</math> and Quaternions'': Cornelia-Livia Bejan, {{zbl|1033.53001}}; Udo Hertrich-Jeromin (2004), { ...4 KB (502 words) - 06:18, 9 August 2024
- ...utions have less error than separable quaternion solutions.<ref name="dual-quaternions"/> ...8 KB (1,204 words) - 17:53, 23 February 2025
- ...with quaternions, and the second about a decade later, as in ''Lectures on Quaternions'' (1853).<ref name=H53/>{{rp|665}} The popular text ''[[Vector Analysis]]'' ...rnell.edu/cgi-bin/cul.math/docviewer?did=05230001&seq=9 |title=Lectures on Quaternions |publisher=Royal Irish Academy}} Link from [[Cornell University]] Historica ...8 KB (1,046 words) - 02:16, 22 October 2022
- ...134-5|postscript=<!--none-->}}. ([http://nugae.wordpress.com/2007/04/25/on-quaternions-and-octonions/ Review]). ...1 KB (196 words) - 10:26, 20 January 2022
- :By the expression ''AB'' = ''NO'', in Linear Algebra and in the science of Quaternions also, it is understood that the length of ''AB'' is equal to that of ''NO'' The book has five chapters and an appendix "Complex quantities and quaternions" in 68 pages with contents listed on page 69. ...8 KB (1,257 words) - 23:02, 12 February 2025
- ...re determinant of a matrix formed from a suitable collection of vectors of quaternions is zero if and only if the vectors are linearly dependent. ...2 KB (234 words) - 02:54, 4 February 2025
- ...s (dimension 1), the field of [[complex number]]s (dimension 2), and the [[quaternions]] (dimension 4). * isomorphic to the quaternions if noncommutative but associative ...8 KB (1,230 words) - 18:39, 1 May 2024
- [[Category:Quaternions]] ...2 KB (240 words) - 10:36, 24 May 2022
- ..., [[harmonic function|harmonicity]] and [[conformality]] in the context of quaternions. Unlike the [[complex number]]s and like the [[real number|reals]], the fou which [[quaternions and spatial rotation|rotates the vector part of ''q'']] by twice the angle ...19 KB (2,798 words) - 12:23, 26 February 2025
- written as a pair of quaternions, <math>\hat {\textbf{Q}}= \textbf{Q} + ...2, P_3, P_4)</math> of the object, the transformation equation in terms of quaternions is given by ...10 KB (1,502 words) - 19:31, 8 August 2023