Complex Numbers in n Dimension

Mathematics Studies

Saul Lubkin

286 pages, parution le 06/11/2002

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Résumé

The work presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this work is the interplay between the algebraic, the geometric and the analytic facets of the relations.

Contents

1 Hyperbolic Complex Numbers in Two Dimensions

Operations with hyperbolic twocomplex numbers
Geometric representation of hyperbolic twocomplex numbers
Exponential and trigonometric forms of a twocomplex number
Elementary functions of a twocomplex variable
Twocomplex power series
Analytic functions of twocomplex variables
Integrals of twocomplex functions
Factorization of twocomplex polynomials
Representation of hyperbolic twocomplex numbers by irreducible matrices

2 Complex Numbers in Three Dimensions

Operations with tricomplex numbers
Geometric representation of tricomplex numbers
The tricomplex cosexponential functions
Exponential and trigonometric forms of tricomplex numbers
Elementary functions of a tricomplex variable
Tricomplex power series
Analytic functions of tricomplex variables
Integrals of tricomplex functions
Factorization of tricomplex polynomials
Representation of tricomplex numbers by irreducible matrices

3 Commutative Complex Numbers in Four Dimensions

Circular complex numbers in four dimensions
Hyperbolic complex numbers in four dimensions
Planar complex numbers in four dimensions
Polar complex numbers in four dimensions

4 Complex Numbers in 5 Dimensions

Operations with polar complex numbers in 5 dimensions
Geometric representation of polar complex numbers in 5 dimensions
The polar 5-dimensional cosexponential functions
Exponential and trigonometric forms of polar 5-complex numbers
Elementary functions of a polar 5-complex variable
Power series of 5-complex numbers
Analytic functions of a polar 5-complex variable
Integrals of polar 5-complex functions
Factorization of polar 5-complex polynomials
Representation of polar 5-complex numbers by irreducible matrices

5 Complex Numbers in 6 Dimensions

Polar complex numbers in 6 dimensions
Planar complex numbers in 6 dimensions

6 Commutative Complex Numbers in n Dimensions

Polar complex numbers in n dimensions
Planar complex numbers in even n dimensions

Caractéristiques techniques

	PAPIER
Éditeur(s)	North-Holland
Auteur(s)	Saul Lubkin
Parution	06/11/2002
Nb. de pages	286
Format	17 x 24,5
Couverture	Relié
Poids	677g
Intérieur	Noir et Blanc
EAN13	9780444511232