谢邦杰教授对体上矩阵理论研究的贡献及其在中国的进展  

Professor Xie Bangjie's contribution to matrices over skew field and its development in China

作　　者：庄瓦金[1] 

机构地区：[1]漳州师范学院数学系,漳州363000

出　　处：《黑龙江大学自然科学学报》2007年第5期607-616,共10页Journal of Natural Science of Heilongjiang University

摘　　要：注意到体上矩阵研究的价值与困难,综述了谢邦杰教授1978-1982年关于体上矩阵相似标准形、弱标准形刻画定理,可中心矩阵的特征值基础、行列式方案,以及自共轭四元数矩阵的行列式理论等研究成果;进而阐述了1980年以来中国学者在这些成果基础上对体上矩阵的秩、相似标准形理论、四元数矩阵行列式、自共轭四元数矩阵,以及体上矩阵方程与广义逆矩阵等研究的进一步推进。With regard to the value and difficulty of research on matrices over skew field, Professor Xie Bangjie＇ s research on matrix similarity canonical form, weak canonical form descriptive theorem, eigenvalue basis of centerable matrices, determinant program and selfconjugate quaternionic matrices over skew field in 1978～1982 are reviewed. Moreover, since 1980 the advancement of Chinese scholars＇study based on these above is surveyed, such as rank of matrices, theory of similarity canonical form, determinant of quaternionic matrices, self - conjugate quaternionic matrices, matrix equations and generalized inverse matrices.

关 键 词：谢邦杰 体上矩阵理论 矩阵相似标准形 特征值 行列式 自共轭四元数矩阵 

分 类 号：O151[理学—数学]