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Biquaternion

In abstract algebra, the biquaternions are the numbers w + x i + y j + z k, where w, x, y, and z are complex numbers, or variants thereof, and the elements of {1, i, j, k} multiply as in the quaternion group and commute with their coefficients. There are three types of biquaternions corresponding to complex numbers and the variations thereof:

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Overview

Definition

Place in ring theory

Algebraic properties

Associated terminology

As a composition algebra

Scalar-vector representation

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Biquaternion

Nodes120
Edges119
Triples34
Avg. degree1.98
Density0.016667
Components1

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Biquaternion

Top relations

related to Associated terminology · 10
Biquaternion → As, But, Just, Let, Lorentz, SO, Such, The, Then, To
related to As a composition algebra · 7
Biquaternion → Adrian Albert, Although, Cayley, Dickson, Hamilton, In, The
related to Definition · 6
Biquaternion → Arthur, Commutativity, Conway, Hamilton, Let, To
related to Scalar-vector representation · 6
Biquaternion → An, Both, In, Sc, There, Vc
related to Subalgebras · 2
Biquaternion → Considering, The
see also · 2
Biquaternion → LambekMacFarlane's, Lorentz TransformationsBiquaternion
related to Algebraic properties · 1
Biquaternion → The

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Important terminology

biquaternions displaystyle algebra complex group numbers quaternions representation lorentz isomorphic real quaternion product subalgebra square one given coefficients unit also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Biquaternionrelated to Algebraic propertiesThe0.60section
Biquaternionrelated to As a composition algebraAlthough0.60section
Biquaternionrelated to As a composition algebraHamilton0.60section
Biquaternionrelated to As a composition algebraAdrian Albert0.60section
Biquaternionrelated to As a composition algebraCayley0.60section
Biquaternionrelated to As a composition algebraDickson0.60section
Biquaternionrelated to As a composition algebraIn0.60section
Biquaternionrelated to As a composition algebraThe0.60section
Biquaternionrelated to Associated terminologyAs0.60section
Biquaternionrelated to Associated terminologyThe0.60section
Biquaternionrelated to Associated terminologyLorentz0.60section
Biquaternionrelated to Associated terminologySuch0.60section

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