首页 | 本学科首页   官方微博 | 高级检索  
     检索      

体上代数矩阵的素有理标准形与特征值
引用本文:黄礼平.体上代数矩阵的素有理标准形与特征值[J].数学学报,1998,41(4):871-880.
作者姓名:黄礼平
作者单位:湘潭工学院基础科学部
基金项目:国家自然科学基金,湖南省自然科学基金
摘    要:本文应用最小中心多项式给出了体上代数矩阵的素有理标准形与初等因子组的构造,由此得到体上代数矩阵相似的充要条件以及相似于一个对角矩阵的充要条件.本文还讨论了体上矩阵的左、右特征值的构造与性质.

关 键 词:体,代数矩阵,初等因子组,最小中心多项式,素有理标准形,右(左)特征值

The Primary Rational Canonical Form and Eigenvalues of Algebraic Matrix over a Skew Field
Huang Liping.The Primary Rational Canonical Form and Eigenvalues of Algebraic Matrix over a Skew Field[J].Acta Mathematica Sinica,1998,41(4):871-880.
Authors:Huang Liping
Institution:Huang Liping (Department of Basic Sciences, Xiangtan Polytechnic University, Xiangtan 411201, China) (Email: hangp@public.xt.hn.cn)
Abstract:Let D be any skew field, by using the minimal central polynomial, this paper gives the structure of the primary rational canonical form and the elementary divisors of any algebraic matrix over D, obtains the necessary and sufficient condition that two algebraic matrices over D are similar, and the necessary and sufficient condition that a algebraic matrix over D is similar to a diagonal matrix. This paper also discusses the structure and properties of the left or right eigenvalue of a matrix over D.
Keywords:Skew field  Algebraic matrix  Elementary divisors    Primary rational canonical form  Minimal central polynomial  Left (right) eigenvalues  
本文献已被 CNKI 维普 等数据库收录!
点击此处可从《数学学报》浏览原始摘要信息
点击此处可从《数学学报》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号