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Split-quaternion

In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They form an associative algebra of dimension four over the real numbers.

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Overview

Definition

Properties

Representation as complex matrices

Generation from split-complex numbers

Stratification

Colour space

Historical notes

Synonyms

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Map overview Semantic statistics

Split-quaternion

Nodes98
Edges97
Triples52
Avg. degree1.98
Density0.020408
Components1

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Split-quaternion

Top relations

related to Synonyms · 13
Split-quaternion → Antiquaternions, Exspherical, In, Ivanov, Macfarlane, Manifolds, Mohaupt, Para-quaternions, Pseudoquaternions, Rosenfeld, Split-quaternions, Yaglom, Zamkovoy
related to Historical notes · 11
Split-quaternion → Bibliography, Clifford, Cockle, Dublin Philosophical Magazine, Edinburgh, He, In, James Cockle, London, Quaternion Association, The
related to Properties · 7
Split-quaternion → As, But, For, Hamilton, Like, So, This
related to Generation from split-complex numbers · 6
Split-quaternion → Adrian Albert, Cayley, Dickson, If, Split-quaternions, The
related to Stratification · 5
Split-quaternion → In, It, Its, Let, One
related to Representation as complex matrices · 3
Split-quaternion → Here, There, This
related to Stratification by the norm · 3
Split-quaternion → As, Their, These
related to Definition · 2
Split-quaternion → By, The
related to Nilpotent case · 2
Split-quaternion → This, With

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Important terminology

split-quaternions displaystyle real algebra matrices form norm numbers matrix nonreal quaternions also isomorphic mathbb complex part nilpotent determinant generated one

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Split-quaternionrelated to DefinitionThe0.60section
Split-quaternionrelated to DefinitionBy0.60section
Split-quaternionrelated to Generation from split-complex numbersSplit-quaternions0.60section
Split-quaternionrelated to Generation from split-complex numbersCayley0.60section
Split-quaternionrelated to Generation from split-complex numbersDickson0.60section
Split-quaternionrelated to Generation from split-complex numbersAdrian Albert0.60section
Split-quaternionrelated to Generation from split-complex numbersThe0.60section
Split-quaternionrelated to Generation from split-complex numbersIf0.60section
Split-quaternionrelated to Historical notesThe0.60section
Split-quaternionrelated to Historical notesJames Cockle0.60section
Split-quaternionrelated to Historical notesLondon0.60section
Split-quaternionrelated to Historical notesEdinburgh0.60section

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