Hypercomplex Numbers: An Elementary Introduction to Algebras - Tapa blanda

Kantor, I.L.; Solodovnikov, A.S.

 
9781461281917: Hypercomplex Numbers: An Elementary Introduction to Algebras
Tapa blanda
ISBN 10: 1461281911 ISBN 13: 9781461281917
Editorial: Springer, 2011

Sinopsis

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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Reseña del editor

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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Editorial
Springer
Año de publicación
2011
Idioma
Inglés
ISBN 10 
1461281911
ISBN 13 
9781461281917
Encuadernación
Tapa blanda
Número de páginas
184
Contacto del fabricante
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Darmstadt
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Alemania

Otras ediciones populares con el mismo título

9780387969800: Hypercomplex Numbers: An Elementary Introduction to Algebras

Edición Destacada

ISBN 10:  0387969802 ISBN 13:  9780387969800
Editorial: Springer Verlag, 1989
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