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Laguerre transformations

The Laguerre transformations or axial homographies are an analogue of Möbius transformations over the dual numbers. When studying these transformations, the dual numbers are often interpreted as repre

Dual number

In algebra, the dual numbers are a hypercomplex number system first introduced in the 19th century. They are expressions of the form a + bε, where a and b are real numbers, and ε is a symbol taken to

Applications of dual quaternions to 2D geometry

In this article, we discuss certain applications of the dual quaternion algebra to 2D geometry. At this present time, the article is focused on a 4-dimensional subalgebra of the dual quaternions which

Hypercomplex number

In mathematics, hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers. The study of hypercomplex numbers in the late 19th centu

Split-complex number

In algebra, a split complex number (or hyperbolic number, also perplex number, double number) has two real number components x and y, and is written z = x + y j, where j2 = 1. The conjugate of z is z∗

Sedenion

In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the real numbers; they are obtained by applying the Cayley–Dickson construction to the octonions

Hypercomplex analysis

In mathematics, hypercomplex analysis is the basic extension of real analysis and complex analysis to the study of functions where the argument is a hypercomplex number. The first instance is function

Hurwitz's theorem (normed division algebras)

No description available.

Multicomplex number

In mathematics, the multicomplex number systems are defined inductively as follows: Let C0 be the real number system. For every n > 0 let in be a square root of −1, that is, an imaginary unit. Then .

Bicomplex number

In abstract algebra, a bicomplex number is a pair (w, z) of complex numbers constructed by the Cayley–Dickson process that defines the bicomplex conjugate , and the product of two bicomplex numbers as

Grassmann number

In mathematical physics, a Grassmann number, named after Hermann Grassmann (also called an anticommuting number or supernumber), is an element of the exterior algebra over the complex numbers. The spe

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