# Category: Hypercomplex numbers

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
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