与对称矩阵可交换的反对称矩阵  

Anti-Symmetric Matrices Which Are Commutative with Symmetric Matrices

作　　者：黄益生[1] 姚海鹭[1] 

机构地区：[1]三明学院数学与计算机科学系,福建三明365004

出　　处：《龙岩学院学报》2010年第2期1-4,8,共5页Journal of Longyan University

基　　金：福建省教育厅高等学校教学质量工程资助项目(ZL09021TZ(SJ))

摘　　要：引入对称矩阵的导出矩阵与次导出矩阵的概念,给出n阶对称矩阵与n阶反对称矩阵是可交换的两个等价条件。同时,利用导出矩阵和次导出矩阵的秩,对3阶对称矩阵进行分类,并且对每一种类型的3阶对称矩阵,求出与它可交换的所有3阶反对称矩阵。In this paper, we introduce the concepts of the induced matrix and sub-induced matrix of a symmetrie matrix, and obtain two equivalent conditions that an n-order symmetric matrix and an n-order antisymmetric matrix are commutative. At the same time, using the ranks of induced matrix and sub-induced matrix, we give a partition of 3-order symmetric matrices. Moreover, for each class of 3-order symmetric matrices, we find all 3-order anti-symmetric matrices which are commutative with this class of matrices.

关 键 词：对称矩阵 反对称矩阵 交换性 导出矩阵 次导出矩阵 

分 类 号：O151[理学—数学]