摘要
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.
出处
《厦门大学学报(自然科学版)》
CAS
CSCD
北大核心
2009年第1期27-30,共4页
Journal of Xiamen University:Natural Science
关键词
四元数体
奇异值分解
双矩阵分解
quaternion field
singular value decomposition
pairwise matrices decomposition