Functions and mappings | Complex analysis

Motor variable

In mathematics, a function of a motor variable is a function with arguments and values in the split-complex number plane, much as functions of a complex variable involve ordinary complex numbers. William Kingdon Clifford coined the term motor for a kinematic operator in his "Preliminary Sketch of Biquaternions" (1873). He used split-complex numbers for scalars in his split-biquaternions. Motor variable is used here in place of split-complex variable for euphony and tradition. For example, Functions of a motor variable provide a context to extend real analysis and provide compact representation of mappings of the plane. However, the theory falls well short of function theory on the ordinary complex plane. Nevertheless, some of the aspects of conventional complex analysis have an interpretation given with motor variables, and more generally in hypercomplex analysis. (Wikipedia).

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Translation (geometry) | Split-complex number | Complex analysis | Hypercomplex analysis | Direct sum of modules | Squeeze mapping | Riemann sphere | Laplace's equation | Exponential function | Split-biquaternion | Unit disk | Identity component | Torus | Homogeneous coordinates | Dual number | Complex plane | Real analysis | Mathematics | Cauchy–Riemann equations | Function (mathematics) | Affine transformation | Isaak Yaglom | Polar decomposition | Stereographic projection | Versor | Wave equation | Isotropic line | Georg Scheffers | Projective line over a ring | Holomorphic function | Harmonic function | Möbius transformation | Corrado Segre | Compact space | Hyperbolic angle | Walter Benz | Complex number | Differential geometry | Hyperboloid | Domain (mathematical analysis) | Émile Borel | Cayley transform | Hyperbolic orthogonality | Unit hyperbola | Range of a function | Multiplicative inverse