线性代数课程增加盖尔圆定理的思考  

Some suggestion on supplementing gerschgorin's disk theorem in linear algebra

作　　者：雍龙泉[1] 

机构地区：[1]陕西理工学院数学系,陕西汉中723001

出　　处：《大庆师范学院学报》2009年第3期66-68,共3页Journal of Daqing Normal University

基　　金：国家自然科学基金项目:不完全信息条件下企业技术创新的自组织机制研究(70472072);陕西省教育厅科学技术研究资助项目:大型电力系统优化调度方法研究(07JK204)

摘　　要：矩阵对角化是线性代数的重要内容,现行课本已经给出了矩阵可对角化的一些条件,利用特征值和特征向量的某些特性来判断矩阵可否对角化。有一类矩阵对角化问题不能用这些方法来证明,为此引入了盖尔圆定理,利用盖尔圆定理可以给出该类矩阵对角化问题的证明。利用盖尔圆定理解决了矩阵论中的一个典型问题,因此在线性代数课程中增加盖尔圆定理是很有必要的。Diagonalization of matrix was an important problem in linear algebra, some conditions on judging diagonalization have been presented, that is using some properties of eigenvalue or eigenvector to determine whether the matrix can be transformed into diagonal matrix or not. In this paper, a new problem whose diagonalization is cannot be proved by above method is given, by using Gerschgorin＇s disk theorem, we solved this problem. Finally, we settled a typical problem in matrix theory by using Gerschgorin＇s disk theorem, too. By above reasons, we illuminate that supplementing Gerschgorin＇s disk theorem is very necessary in linear algebra.

关 键 词：线性代数 矩阵对角化问题 盖尔圆定理 

分 类 号：O151.2[理学—数学]