由此，把复数域上矩阵论的若干重要定理推广到了四元数体。
Accordingly, we extended several important theorems of complex matrix theory to the quaternion field.
本文对四元数体上矩阵奇异值摄动定理给出了推广，且这些结果对复矩阵也是新的。
The quaternion matrix singular value perturbation theorem is generalized and these results are also new one for complex matrix.
讨论实四元数体上方阵的右特征值，并将域上矩阵的一些相应结果推广到实四元数体上。
The right characteristic values of matrices on quaternion division algebra are discussed, and some corresponding results for complex matrices are generalized and improved.
证明了任一环有代数封闭的扩张环，且实封闭域上的四元数体是代数封闭的，给出了代数封闭环的若干性质。
The two theorems are proved that any ring can be extended into an algebraically closed ring and that the quaternionic skew field over a real closed field is algebraically closed.
同时得到一些关于四元数矩阵的性质，以及体上矩阵相似和合相似的充要条件。
Finally, the necessary and sufficient condition is shown for similarity and consimilarity of matrices over quaternion field.
用文中提出的体绘制算法绘制了三元数法和四元代数法所构造的三维M集。
Finally, the 3-d M-sets generated by the ternary number and quaternion algebra are both rendered by our new algorithm.
用文中提出的体绘制算法绘制了三元数法和四元代数法所构造的三维M集。
Finally, the 3-d M-sets generated by the ternary number and quaternion algebra are both rendered by our new algorithm.
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