关于矩阵族的一致相随性探讨  

The Discussion of Consistent Accompany on Family of Matrices

作　　者：邓勇[1] 

机构地区：[1]喀什师范学院数学系,新疆喀什844006

出　　处：《重庆师范大学学报（自然科学版）》2014年第4期78-81,共4页Journal of Chongqing Normal University:Natural Science

基　　金：新疆维吾尔自治区高校科研计划重点项目(No.XJEDU2008Ⅰ31)

摘　　要：矩阵的对角化问题是高等代数中一个重要而基本的内容,通常文献只讨论一个给定方阵的可对角化条件。但在理论与应用中往往会大量涉及矩阵族的同时三角化问题。因此,研究矩阵族可同时三角化的条件将是一个不可回避的课题。另外有文献虽引入了相似矩阵可同时对角化的概念及判定条件,但实际上矩阵族同时三角化和同时对角化在论证上差异却很大。为此,在已有研究的基础上,引入了矩阵族的一致相随定义,利用特征分析技术研究了矩阵族可同时三角化问题,得到了一致相随存在性的一个定理及其证明,最后例举了一致相随关系的两个应用。The diagonalization of matrix is an important and basic content in advanced algebra, but the diagonalizable conditions of given a square matrix have only discussed in common advanced algebra textbooks and literatures. However, a set of matrices were often heavily involved in theories and applications. Therefore, people look for conditions that a set of matrices triangularization sim- ultaneously will be an unavoidable, topic. Although the concepts and judged conditions of triangularization simultaneously on a set of matrices were introduced in [1], but see from the surface, triangularization and diagonalization simultaneously on a set of matrices seem to be similar themes of commutative matrix family. However, there are larger differences about their argumentations in fact. Clearly, we discuss the conditions of simultaneously triangularization on a set of matrices must be another way. To this end, The definition was introduced about consistent accompany of matrix family based on literatures [2-3], use it to study the problems of the matrix family similar triangulation simultaneously, obtained an existence theorem and its proof, and then given two of applications on consistent accompany.

关 键 词：可交换矩阵族 一致相随 不变子空间 三角化 SCHUR分解 

分 类 号：O151[理学—数学]