Biquaternion (complexified quaternion) roots of-1

被引：36

作者：

Sangwine, Stephen J. ^{[1
]}

机构：

[1] Univ Essex, Dept Elect Syst Engn, Colchester CO7 9EU, Essex, England

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2006年 / 16卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

D O I：

10.1007/s00006-006-0005-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The roots of -1 in the set of biquaternions (quaternions with complex components, or complex numbers with quaternion real and imaginary parts) are derived. There are trivial solutions (the complex operator, and any unit pure real quaternion), and non-trivial solutions consisting of complex numbers with perpendicular pure quaternion real and imaginary parts. The moduli of the two perpendicular pure quaternions are expressible by a single parameter by using a hyperbolic trigonometric identity.

引用

页码：63 / 68

页数：6