Hypercomplex Numbers. An Elementary Introduction to Algebras. Translated by A. Shenitzer.

Kantor, I. L. (Isai L`vovich) and A. S. (Aleksandr Samuilovich) Solodovnikov:

ISBN 10: 0387969802 / ISBN 13: 9780387969800

Published by New York, Berlin, Heidelberg, London usw.: Springer-Verlag, 1989

About this Item

X, 169 Seiten, Fadenheftung, Format 16 x 24,2 cm, hartgebundener u. glanzkaschierter Original-Pappband. * Zweite ISBN: 3-540-96980-2. Erhaltung: Keine Mängel, praktisch wie neu [Eine größere Sammlung Physik, Mathematik, Astronomie und verwandte Gebiete wird derzeit in den Bestand eingearbeitet. Sie finden diese Titel bei uns in den gleichnamigen Rubriken]. Sprache: Englisch.

Seller Inventory # 29781

Bibliographic Details

• Title: Hypercomplex Numbers. An Elementary Introduction to Algebras. Translated by A. Shenitzer.
• Publisher: New York, Berlin, Heidelberg, London usw.: Springer-Verlag
• Publication Date: 1989
• ISBN 10: 0387969802
• ISBN 13: 9780387969800
• Edition: 1st Edition
• Seller catalogs:
  • Mathematik

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)