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- Biquaternion abstract "In abstract algebra, the biquaternions are the numbers w + x i + y j + z k, 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 biquaternion: (Ordinary) biquaternions when the coefficients are (ordinary) complex numbers Split-biquaternions when w, x, y, and z are split-complex numbers Dual quaternions when w, x, y, and z are dual numbers.This article is about the ordinary biquaternions named by William Rowan Hamilton in 1844 (see Proceedings of Royal Irish Academy 1844 & 1850 page 388). Some of the more prominent proponents of these biquaternions include Alexander Macfarlane, Arthur W. Conway, Ludwik Silberstein, and Cornelius Lanczos. As developed below, the unit quasi-sphere of the biquaternions provides a presentation of the Lorentz group, which is the foundation of special relativity.The algebra of biquaternions can be considered as a tensor product C ⊗ H (taken over the reals) where C is the field of complex numbers and H is the algebra of (real) quaternions. In other words, the biquaternions are just the complexification of the (real) quaternions. Viewed as a complex algebra, the biquaternions are isomorphic to the algebra of 2×2 complex matrices M2(C). They can be classified as the Clifford algebra Cℓ2(C) = Cℓ03(C). This is also isomorphic to the Pauli algebra Cℓ3,0(R), and the even part of the spacetime algebra Cℓ01,3(R).".
- Biquaternion wikiPageExternalLink books?id=fIRAAAAAIAAJ.
- Biquaternion wikiPageExternalLink books?id=ggoFAAAAQAAJ&pg=PA388&dq=proceedings+of+royal+irish+academy+1844+Hamilton&hl=en&ei=WysiTPLwMcKRnwepmoDBDw&sa=X&oi=book_result&ct=result&resnum=5&ved=0CD4Q6AEwBA.
- Biquaternion wikiPageExternalLink math.
- Biquaternion wikiPageExternalLink 2369176.
- Biquaternion wikiPageID "1207070".
- Biquaternion wikiPageRevisionID "606358631".
- Biquaternion hasPhotoCollection Biquaternion.
- Biquaternion subject Category:Articles_containing_proofs.
- Biquaternion subject Category:Quaternions.
- Biquaternion subject Category:Ring_theory.
- Biquaternion subject Category:Special_relativity.
- Biquaternion type Abstraction100002137.
- Biquaternion type DefiniteQuantity113576101.
- Biquaternion type Digit113741022.
- Biquaternion type Four113744304.
- Biquaternion type Integer113728499.
- Biquaternion type Measure100033615.
- Biquaternion type Number113582013.
- Biquaternion type Quaternions.
- Biquaternion comment "In abstract algebra, the biquaternions are the numbers w + x i + y j + z k, where w, x, y, and z are complex numbers and the elements of {1, i, j, k} multiply as in the quaternion group.".
- Biquaternion label "Biquaternion".
- Biquaternion label "Biquaternion".
- Biquaternion label "Biquaternion".
- Biquaternion label "Бикватернион".
- Biquaternion sameAs Biquaternion.
- Biquaternion sameAs Biquaternion.
- Biquaternion sameAs Bikuaternion.
- Biquaternion sameAs m.04h98h.
- Biquaternion sameAs Q2590607.
- Biquaternion sameAs Q2590607.
- Biquaternion sameAs Biquaternion.
- Biquaternion wasDerivedFrom Biquaternion?oldid=606358631.
- Biquaternion isPrimaryTopicOf Biquaternion.