Hypercomplex Numbers

Name: Hypercomplex Numbers
Brand: Springer-Verlag New York Inc.
SKU: 9781461281917
Price: 550.06 PLN
Availability: InStock

An Elementary Introduction to Algebras

Autor: I. L. Kantor, A. S. Solodovnikov

Język:

Oprawa: Miękka

Wydawca: Springer-Verlag New York Inc.

Dostępność: Dostępna u dostawcy

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This book deals with various systems of "numbers" that can be constructed by adding "imaginary units...

Informacje o książce

Autor

I. L. Kantor, A. S. Solodovnikov

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2011

strony

169

EAN

9781461281917

ISBN

1461281911

Enbook ID

06795594

Wydawca

Springer-Verlag New York Inc.

Waga

289

Wymiary

155 x 235 x 11

Pełny opis

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).

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Hypercomplex Numbers

An Elementary Introduction to Algebras

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