On Bicomplex Representation Methods and Applications of Matrices over Quaternionic Division Algebra

摘要

In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a new inverse concept of quaternion matrix and a new similar matrix concept. Under the new concept system, many quaternion algebra problems can be transformed into complex algebra problems to express and study. These concepts can perfect the theory of [J.L. Wu, A new representation theory and some methods on quaternion division algebra, JP Journal of Algebra, 2009, 14(2): 121-140] and unify the complex algebra and quaternion division algebra.