algebra isomorphic to the direct sum H ⊕ H, the split-biquaternions. One can also study Clifford algebras on complex vector spaces. Every nondegenerate...

K. Clifford obtained a broad generalization of these numbers that he called biquaternions, which is an example of what is now called a Clifford algebra...

{\displaystyle \mathbb {C} } ) (2 × 2 complex matrices, biquaternions, Pauli algebra). All of the Clifford algebras Clp,q( R {\displaystyle \mathbb {R} } ) apart...

which included presentation of biquaternions. The following passage from page 673 shows how Hamilton uses biquaternion algebra and vectors from quaternions...

numbers. William Kingdon Clifford coined the term motor for a kinematic operator in his "Preliminary Sketch of Biquaternions" (1873). He used split-complex...

extend the concept to 4-space. Problems in that algebra led to use of biquaternions after 1900. In a widely seen review, Macfarlane wrote: ... the root...

Pearson/Addison Wesley. pp. 300–307. ISBN 978-0805387322. Poisson, Eric; Will, Clifford M. (2014-05-29). Gravity:Newtonian, Post-Newtonian, Relativistic. Cambridge...

Magnetism. In 1878 William Kingdon Clifford published his Elements of Dynamic. Clifford developed split-biquaternions (e.g. q = w + x i + y j + z k {\displaystyle...

84:27–48. William Kingdon Clifford (1882) Mathematical Works, A. W. Tucker editor, page 392, "Further Notes on Biquaternions" V.Cruceanu, P. Fortuny &...

Clifford M (2010). "Relativity". Grolier Multimedia Encyclopedia. Archived from the original on 21 May 2020. Retrieved 1 August 2010. Will, Clifford M...

in the Universe. Cambridge U Press. ISBN 978-0-521-81405-8. Pickover, Clifford (1998). Black Holes: A Traveler's Guide. Wiley, John & Sons, Inc. ISBN 978-0-471-19704-1...

Vahlen also recounts split-biquaternions and parabolic biquaternions originated by Clifford. But Vahlen cites Eduard Study most of all since Study also...

Charles-Ange Laisant and Alexander Macfarlane. William K. Clifford expanded the types of biquaternions, and explored elliptic space, a geometry in which the...

Plane-based geometric algebra is an application of Clifford algebra to modelling planes, lines, points, and rigid transformations. Generally this is with...

that ring. Arthur Conway, one of the early adopters of relativity via biquaternion transformations, considered the quaternion-multiplicative-inverse transformation...

representation of the action of the Lorentz group on Minkowski space uses biquaternions, which form a composition algebra. The isometry property of Lorentz...

open and keep timelike geodesic free float "warp drives" working. With Clifford Will and others of his students, he laid the foundations for the theoretical...

algebraic structures, such as a tensor product of two copies of the biquaternions, or the algebra of 4 × 4 matrices over the real numbers, or that studied...

Equations and their Solutions", in Ablamowicz, Rafał; Lounesto, Pertti (eds.), Clifford Algebras and Spinor Structures, Springer, pp. 265–280, doi:10.1007/978-94-015-8422-7_16...

Will, Clifford M. (1993), Theory and experiment in gravitational physics, Cambridge University Press, ISBN 978-0-521-43973-2 Will, Clifford M. (2006)...

therefore a ring, also a division ring and a domain. It is a special case of a Clifford algebra, classified as Cl 0 , 2 ⁡ ( R ) ≅ Cl 3 , 0 + ⁡ ( R ) . {\displaystyle...

(1984) The University of Chicago Press, Chicago. See Section 3.3. Will, Clifford. Theory and Experiment in Gravitational Physics, p. 143 (Cambridge University...

San Francisco: W. H. Freeman. ISBN 0-7167-0344-0. See Box 39.1. Will, Clifford M. (1986). "Chapter 8: The Rise and Fall of the Brans–Dicke Theory". Was...

Lifshitz, E.M., The Classical Theory of Fields (Pergamon Press), 1987. Will, Clifford M. (2014). "The Confrontation between General Relativity and Experiment"...

how spin representations of the Lorentz Lie algebra can be embedded in Clifford algebras. The Lorentz group has also historically received special attention...

ISBN 978-3-540-41236-6. S2CID 15430387. {{cite book}}: |journal= ignored (help) Will, Clifford M. (December 2014). "The Confrontation between General Relativity and Experiment"...

this to include seven parameters in papers published in 1968 and 1969. Clifford Martin Will introduced a stressed, continuous matter description of celestial...

ISBN 0-7167-6034-7 Will, Clifford M. (1993), Was Einstein Right?, Oxford University Press, ISBN 0-19-286170-0 Will, Clifford M. (2006), "The Confrontation...

tessarines in 1848 and coquaternions in 1849. William Kingdon Clifford introduced split-biquaternions in 1873. In addition Cayley introduced group algebras over...

Zerilli–Wheeler equation, Wheeler–DeWitt equation, textbook), Paul S. Wesson (relativistic cosmology, Kaluza–Klein theory) Clifford Martin Will (parametrized...