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Hypercomplex Numbers
I.L. Kantor, A.S. Solodovnikov (Taschenbuch, Englisch)
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Beschreibung
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). 139,09 €
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Technische Daten
Erscheinungsdatum
21.09.2011
Sprache
Englisch
EAN
9781461281917
Herausgeber
Springer US
Sonderedition
Nein
Autor
I.L. Kantor, A.S. Solodovnikov
Seitenanzahl
169
Einbandart
Taschenbuch
Buch Untertitel
An Elementary Introduction to Algebras
Übersetzt von
Abe Shenitzer
Schlagwörter
matrix theory
Thema-Inhalt
PBF - Algebra
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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