Hypercomplex numbers : an elementary introduction to algebras
著者
書誌事項
Hypercomplex numbers : an elementary introduction to algebras
Springer-Verlag, c1989
- : us
- : gw
- タイトル別名
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Giperkompleksnye chisla
大学図書館所蔵 全29件
注記
Translation of: Giperkompleksnye Čisla. Nauka, Moscow, 1973
内容説明・目次
内容説明
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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