Hypercomplex Numbers : An Elementary Introduction to Algebras

I. L. Kantor

ISBN 10: 1461281911 / ISBN 13: 9781461281917

Published by Springer New York, Springer US, 2011

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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).

Seller Inventory # 9781461281917

Bibliographic Details

• Title: Hypercomplex Numbers : An Elementary Introduction to Algebras
• Publisher: Springer New York, Springer US
• Publication Date: 2011
• Language: English
• ISBN 10: 1461281911
• ISBN 13: 9781461281917
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 11D millimeters 235 millimeters width by 155 millimeters height by 11 millimeters depth
• Weight: 289 grams

About this title

Synopsis

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).

Language Notes

Text: English, Russian (translation)