关于四元数体上的双矩阵分解

The Decomposition of Pairwise Matrices over a Quaternion Field

利用四元数矩阵的奇异值分解及其转换形式,以及体上矩阵秩的有关结论,使用分块矩阵独有的技巧方法,得到四元数体上具有相同行数或相同列数的矩阵分解定理,其形式均为更有意义的拟对角标准形形式.其结论较大程度地改进和深化相应的实、复数域和体上矩阵的结果.

This paper proved quaternion matrix,which has the same numbers of rows or columns,decomposition theorem by applying the transfer form of the singular value decomposition （SVD） over quaternion matrix, the relational conclusion about rank of matrix over a skew field and the particular skills of partitioned matrix. The form is the canonical form of quasi-diagonal matrix,which is more meaningful. The conclusions of this paper improve and generalize the corresponding results over the field of real numbers, the field of complex numbers or the quaternion field.