特殊双曲型交换四元数矩阵的特征值及逆矩阵

The eigenvalues and inverse matrix of special hyperbolic commutative quaternion matrix

利用特殊双曲型交换四元数的实表示,首先给出了特殊双曲型交换四元数矩阵的实表示及系列性质;其次得到了此类矩阵特征值存在的充分必要条件;最后给出求特殊双曲型交换四元数矩阵的逆矩阵的新方法,并利用算例说明了结论的正确性.

In the paper,using the real representation of special hyperbolic commutative quaternions,firstly,the real representation and series properties of special hyperbolic commutative quaternion matrix are given.Secondly,the sufficient and necessary conditions for the existence of such matrix eigenvalues are obtained.Finally,a new method for the inverse matrix of special hyperbolic commutative quaternion matrix is given,and the correctness of the conclusion is illustrated by an example.