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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Hypercomplex Numbers: An Elementary Introduction to Algebras

Hypercomplex Numbers: An Elementary Introduction to Algebras

Kantor, I. L.
Solodovnikov, A. S.
Shenitzer, Abe

Paperback

Algebra

ISBN10: 1461281911
ISBN13: 9781461281917
Publisher: Springer
Published: Sep 21 2011
Pages: 169
Weight: 0.59
Height: 0.39 Width: 6.14 Depth: 9.21
Language: English
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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