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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.
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- Biquaternion wikiPageExternalLink math.
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- Biquaternion wikiPageRevisionID "700018037".
- Biquaternion wikiPageWikiLink Abstract_algebra.
- Biquaternion wikiPageWikiLink Advances_in_Applied_Clifford_Algebras.
- Biquaternion wikiPageWikiLink Alexander_Macfarlane.
- Biquaternion wikiPageWikiLink Algebra_over_a_field.
- Biquaternion wikiPageWikiLink American_Journal_of_Mathematics.
- Biquaternion wikiPageWikiLink Arthur_Eddington.
- Biquaternion wikiPageWikiLink Arthur_W._Conway.
- Biquaternion wikiPageWikiLink Associative_property.
- Biquaternion wikiPageWikiLink Basis_(linear_algebra).
- Biquaternion wikiPageWikiLink Bicomplex_number.
- Biquaternion wikiPageWikiLink Biquaternion_algebra.
- Biquaternion wikiPageWikiLink Bivector_(complex).
- Biquaternion wikiPageWikiLink Category:Articles_containing_proofs.
- Biquaternion wikiPageWikiLink Category:Quaternions.
- Biquaternion wikiPageWikiLink Category:Ring_theory.
- Biquaternion wikiPageWikiLink Category:Special_relativity.
- Biquaternion wikiPageWikiLink Charles_Jasper_Joly.
- Biquaternion wikiPageWikiLink Clifford_algebra.
- Biquaternion wikiPageWikiLink Closure_(mathematics).
- Biquaternion wikiPageWikiLink Commutative_property.
- Biquaternion wikiPageWikiLink Commutator.
- Biquaternion wikiPageWikiLink Complex_conjugate.
- Biquaternion wikiPageWikiLink Complex_number.
- Biquaternion wikiPageWikiLink Complexification.
- Biquaternion wikiPageWikiLink Cornelius_Lanczos.
- Biquaternion wikiPageWikiLink Dihedral_group.
- Biquaternion wikiPageWikiLink Dimension.
- Biquaternion wikiPageWikiLink Dual_number.
- Biquaternion wikiPageWikiLink Dual_quaternion.
- Biquaternion wikiPageWikiLink EPL_(journal).
- Biquaternion wikiPageWikiLink Euclidean_distance.
- Biquaternion wikiPageWikiLink European_Journal_of_Physics.
- Biquaternion wikiPageWikiLink Exponential_map_(Lie_theory).
- Biquaternion wikiPageWikiLink Field_(mathematics).
- Biquaternion wikiPageWikiLink Frame_of_reference.
- Biquaternion wikiPageWikiLink Group_action.
- Biquaternion wikiPageWikiLink Group_representation.
- Biquaternion wikiPageWikiLink Hyperbolic_angle.
- Biquaternion wikiPageWikiLink Hyperbolic_geometry.
- Biquaternion wikiPageWikiLink Hyperbolic_quaternion.
- Biquaternion wikiPageWikiLink Hyperboloid.
- Biquaternion wikiPageWikiLink Hyperboloid_model.
- Biquaternion wikiPageWikiLink Hypercomplex_number.
- Biquaternion wikiPageWikiLink Identity_matrix.
- Biquaternion wikiPageWikiLink Imaginary_unit.
- Biquaternion wikiPageWikiLink Isomorphism.
- Biquaternion wikiPageWikiLink JSTOR.
- Biquaternion wikiPageWikiLink Lie_algebra.
- Biquaternion wikiPageWikiLink Lie_group.
- Biquaternion wikiPageWikiLink Lie_theory.
- Biquaternion wikiPageWikiLink Linear_algebra.
- Biquaternion wikiPageWikiLink Linear_subspace.
- Biquaternion wikiPageWikiLink Longman.
- Biquaternion wikiPageWikiLink Lorentz_group.
- Biquaternion wikiPageWikiLink Lorentz_transformation.
- Biquaternion wikiPageWikiLink Ludwik_Silberstein.
- Biquaternion wikiPageWikiLink Magma_(algebra).
- Biquaternion wikiPageWikiLink Mathematical_physics.
- Biquaternion wikiPageWikiLink Matrix_ring.
- Biquaternion wikiPageWikiLink Minkowski_space.
- Biquaternion wikiPageWikiLink Musean_hypernumber.
- Biquaternion wikiPageWikiLink Möbius_transformation.
- Biquaternion wikiPageWikiLink Normal_subgroup.
- Biquaternion wikiPageWikiLink One-parameter_group.
- Biquaternion wikiPageWikiLink Orthogonal_group.
- Biquaternion wikiPageWikiLink Pauli_matrices.
- Biquaternion wikiPageWikiLink Philosophical_Magazine.
- Biquaternion wikiPageWikiLink Quantum_mechanics.
- Biquaternion wikiPageWikiLink Quaternion.
- Biquaternion wikiPageWikiLink Quaternion_group.
- Biquaternion wikiPageWikiLink Quaternions_and_spatial_rotation.
- Biquaternion wikiPageWikiLink Quotient_group.
- Biquaternion wikiPageWikiLink Quotient_ring.
- Biquaternion wikiPageWikiLink Rapidity.
- Biquaternion wikiPageWikiLink Ring_(mathematics).
- Biquaternion wikiPageWikiLink Ring_homomorphism.
- Biquaternion wikiPageWikiLink Six-dimensional_space.
- Biquaternion wikiPageWikiLink Spacetime_algebra.
- Biquaternion wikiPageWikiLink Special_linear_group.
- Biquaternion wikiPageWikiLink Special_relativity.
- Biquaternion wikiPageWikiLink Speed_of_light.
- Biquaternion wikiPageWikiLink Spinor.
- Biquaternion wikiPageWikiLink Split-biquaternion.
- Biquaternion wikiPageWikiLink Split-complex_number.
- Biquaternion wikiPageWikiLink Split-quaternion.
- Biquaternion wikiPageWikiLink Subalgebra.
- Biquaternion wikiPageWikiLink Subgroup.
- Biquaternion wikiPageWikiLink Tensor_product_of_algebras.
- Biquaternion wikiPageWikiLink Topological_group.
- Biquaternion wikiPageWikiLink Topology.
- Biquaternion wikiPageWikiLink Unit_(ring_theory).