JP Journal of Algebra, Number Theory and Applications
Volume 14, Issue 2, Pages 121 - 140
(August 2009)
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A NEW REPRESENTATION THEORY AND SOME METHODS ON QUATERNION DIVISION ALGEBRA
Wu Junliang (P. R. China) and Wang Yong (P. R. China)
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Abstract: In this paper, a new representation theory of quaternion matrices is introduced. The new multiplication concept of quaternion matrices, the new determinant concept, the new inverse concept of quaternion matrix and the new similar matrix concept are established on quaternion division algebra. Under the new concepts system, many quaternion algebra problems can be transformed into real algebra problems to express and study. Finally, some methods and conclusions which are entirely different from the previous quaternion theory are presented. We also point out that the new concepts system is not suitable for real matrix and the complex matrix case, because the real matrix and the complex matrix belong to the commutative algebra family but the quaternion matrices belong to the non-commutative algebra family. |
Keywords and phrases: quaternion determinant, product of quaternion matrix, inverse of quaternion matrix, similar quaternion matrix, new concepts system, application. |
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