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Hypercomplex Numbers: An Elementary Introduction to Algebras by A.S. Solodovnikov, I.L. Kantor (Paperback, 2011)

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Product Information

This book deals with various systems of numbers that can be constructed by adding imaginary units to the real numbers. The complex numbers are a classical example of such a system. One of the most important properties of the complex numbers is given by the identity (1) Izz'l = Izl*Iz'I* It says, roughly, that the absolute value of a product is equal to the product of the absolute values of the factors. If we put z = al + a2i, z' = b+ bi, 1 2 then we can rewrite (1) as The last identity states that the product of a sum of two squares by a sum of two squares is a sum of two squares. It is natural to ask if there are similar identities with more than two squares, and how all of them can be described. Already Euler had given an example of an identity with four squares. Later an identity with eight squares was found. But a complete solution of the problem was obtained only at the end of the 19th century. It is substantially true that every identity with n squares is linked to formula (1), except that z and z' no longer denote complex numbers but more general numbers where i,j, . . . , I are imaginary units. One of the main themes of this book is the establishing of the connection between identities with n squares and formula (1).

Product Identifiers

PublisherSpringer-Verlag New York Inc.

ISBN-139781461281917

eBay Product ID (ePID)117423499

Product Key Features

Number of Pages169 Pages

LanguageEnglish

Publication NameHypercomplex Numbers: an Elementary Introduction to Algebras

Publication Year2011

SubjectMathematics

TypeTextbook

AuthorA.S. Solodovnikov, I.L. Kantor

FormatPaperback

Dimensions

Item Height235 mm

Item Weight289 g

Item Width155 mm

Additional Product Features

Country/Region of ManufactureUnited States

Title_AuthorA.S. Solodovnikov, I.L. Kantor