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Split-complex number

In algebra, a split-complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit j satisfying j 2 = 1 {\displaystyle j^{2}=1} , where j ≠ ± 1 {\displaystyle j\neq \pm 1} . A split-complex number has two real number components x and y, and is written z = x + y j . {\displaystyle z=x+yj.} The conjugate of z is z ∗…

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Overview

Definition

Geometry

Algebraic properties

Matrix representations

History

Synonyms

Advanced semantic analysis

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Split-complex number

Nodes110
Edges109
Triples62
Avg. degree1.98
Density0.018182
Components1

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Split-complex number

Top relations

related to Synonyms · 34
Split-complex number → Antonuccio, Bencivenga, Benz, Boehning, Borota, Carmody, Clifford, Cree, Cruceanu, Different, Fjelstad, Fortuny, Gadea, Harvey, Hazewinkel, James Cockle, Kantor, LeClair, Lorentz, Lounesto
related to history · 10
Split-complex number → Clifford, Extending, He, In, James Cockle, Lorentz, Simultaneity, Since, The, William Kingdon Clifford
related to Matrix representations · 7
Split-complex number → I2, IJ, J2, JI, The, Then, Using
related to Geometry · 4
Split-complex number → Euclidean, Just, Minkowski, The
related to Isomorphism · 2
Split-complex number → On, The
is a · 1
Split-complex number → ordered pair of real numbers
related to Algebraic properties · 1
Split-complex number → As

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Important terminology

displaystyle split-complex numbers number algebra hyperbolic mathbb form real complex called plane two hyperbola conjugate multiplication right lvert rvert basis

Entity relationships Subject–Predicate–Object triples

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SubjectPredicateObjectConfidenceSrc
Split-complex numberis aordered pair of real numbers0.90text
λ have been called hyperbolic versors.Since λ has modulus 1instance ofNumbers0.80text
multiplying any split-complex number z by λ preserves the modulus of zinstance ofNumbers0.80text
represents a hyperbolic rotationinstance ofNumbers0.80text
Split-complex numberrelated to Algebraic propertiesAs0.60section
Split-complex numberrelated to GeometryMinkowski0.60section
Split-complex numberrelated to GeometryJust0.60section
Split-complex numberrelated to GeometryEuclidean0.60section
Split-complex numberrelated to GeometryThe0.60section
Split-complex numberrelated to historyThe0.60section
Split-complex numberrelated to historyJames Cockle0.60section
Split-complex numberrelated to historyWilliam Kingdon Clifford0.60section

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