In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They...
22 KB (3,202 words) - 01:53, 4 November 2023
In mathematics, a quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a...
10 KB (1,532 words) - 15:42, 21 February 2024
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton...
96 KB (12,654 words) - 08:09, 19 July 2024
polynomial f ∈ k[x1, ..., xn]. There is a hyperboloid of idempotents in the split-quaternion ring.[citation needed] A partial list of important types of idempotents...
18 KB (2,175 words) - 16:34, 10 May 2024
Versor (redirect from Unit quaternion)
In mathematics, a versor is a quaternion of norm one (a unit quaternion). Each versor has the form q = exp ( a r ) = cos a + r sin a , r 2 = − 1...
19 KB (2,804 words) - 22:37, 12 July 2024
In group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset {...
26 KB (3,724 words) - 08:50, 20 June 2024
spins. Clifford introduced the use of split-complex numbers as coefficients in a quaternion algebra now called split-biquaternions. He called its elements...
27 KB (4,058 words) - 08:04, 26 August 2024
In mathematics, the dual quaternions are an 8-dimensional real algebra isomorphic to the tensor product of the quaternions and the dual numbers. Thus...
31 KB (4,774 words) - 19:01, 9 August 2024
just as the quaternion algebra H can be viewed as a union of complex planes, so the hyperbolic quaternion algebra is a pencil of planes of split-complex numbers...
14 KB (2,107 words) - 03:10, 19 April 2024
Cayley–Dickson construction (category Historical treatment of quaternions)
original Cayley–Dickson construction to the split-complexes also results in the split-quaternions and then the split-octonions. Albert (1942, p. 171) gave a...
18 KB (2,224 words) - 05:25, 6 July 2024