关于复分裂四元数的复矩阵表示及其求逆方法

On the Complex Matrix Representation of Complex Split Quaternions and Its Inversion Method

分裂四元数环是一个非交换代数.为了突破分裂四元数环代数结构中元素的非交换性瓶颈,对其元素进行各种表示是一种通行的做法.为此,引入了复分裂四元数,并证明了它可由4×4复矩阵表示.在此基础上,给出了其代数基本性质和求逆方法.

It is well known that,the ring of split quaternions is a non-commutative algebra.In order to break through the non-commutative bottleneck of elements in this algebraic structure,it is a common practice to take various representations of its elements.Therefore,this paper introduces the complex split quaternion and proves that it can be represented by 4×4 complex matrix representation.On this basis,its basic algebraic properties and inversion methods are given.