[1]唐晓文,杨忠鹏,陈梅香.秩与非零特征值个数的差为1或2的矩阵的性质[J].福建理工大学学报,2015,13(04):388-391.[doi:10.3969/j.issn.1672-4348.2015.04.017]
　Tang Xiaowen,Yang Zhongpeng,Chen Meixiang.Characterization of matrices with the differences between ranks and numbers of nonzero eigenvalues being equal to 1 or 2[J].Journal of Fujian University of Technology;,2015,13(04):388-391.[doi:10.3969/j.issn.1672-4348.2015.04.017]
点击复制

秩与非零特征值个数的差为1或2的矩阵的性质()
分享到：

《福建理工大学学报》[ISSN:2097-3853/CN:35-1351/Z]

卷:
第13卷
期数:
2015年04期
页码:
388-391
栏目:
出版日期:
2015-08-25

文章信息/Info

Title:
Characterization of matrices with the differences between ranks and numbers of nonzero eigenvalues being equal to 1 or 2
作者:
唐晓文; 杨忠鹏; 陈梅香
福建工程学院数理学院
Author(s):
Tang Xiaowen;  Yang Zhongpeng;  Chen Meixiang
College of Mathematics and Physics, Fujian University of Technology
关键词:
矩阵秩;  矩阵指数;  非零特征值;  Jordan标准形
Keywords:
matrix rank;  matrix index;  non-zero eigenvalue;  Jordan form
分类号:
O151.21
DOI:
10.3969/j.issn.1672-4348.2015.04.017
文献标志码:
A
摘要:
以矩阵方幂的秩为基本工具，对秩与非零特征值个数的差为1或2的矩阵做了等价刻画。作为应用，只用矩阵的秩可给出相应矩阵的 Jordan标准形。
Abstract:
With the rank of matrix square power as a basic tool, some equivalent characterization of matrices was presented, in which the differences between the rank and number of non-zero eigenvalues is equal to 1 or 2. As applications, Jordan canonical form of the matrices can be given simply by the rank of the matrices.

参考文献/References:

[1] Nikuie M, Mirnia M K, Mahmoudi Y. Some results about the index of matrix and Drazin inverse[J]. Mathematical Sciences,2010,4(3 ):83-294.
[2] Bernstein D S. Matrix mathematics theory, facts, and formulas[M]. 2nd edi. Princeton:Princeton University press,2009.
[3] Wang G, Wei Y, Qian S. Generalized Inverse Theory and Computations[M]. Beijing:Science Press,2003.
[4] 张景晓.矩阵的秩与其非零特征值个数相等的条件[J].德州学院学报,2012,28(4):6-8.
[5] 梁小春,陈梅香,杨忠鹏,等.矩阵的秩和非零特征值个数关系的进一步讨论[J].闽南师范大学学报：自然科学版，2014，27(2):1-6.
[6] 吕洪斌,杨忠鹏,冯晓霞.矩阵的秩和非零特征值个数差的确定[J].吉林大学学报：理学版,2014，52（6）：1210-1214.
[7] Chen MeiXiang, Lü HongBin, Feng XiaoXia, et al. The essential (m, l)idempotent matrix and its minimal polynomial[J]. International Journal of Applied Mathematics and Statistics, 2013，41（11）:31-41.
[8] Horn R A, Johnson C R. Matrix Analysis[M].New York:Cambridge University Press,1985.
[9] Wu Yan, Linder D F. On the eigenstructures of functional Kpotent matrices and their integral forms[J]. WSEAS Trans Math, 2010,9(4)：244-253.
[10] 胡付高,杨娇.幂零矩阵的一个性质[J].高等数学研究，2011,14(3)：52-54.
[11] Zhang Fuzhen.Matrix Theory: Basic Results and Techniques[M]. 2nd edi. Berlin:Springer, 2011.
[12] 廖小莲，伍征斌，陈国华.k－幂零矩阵的一个新性质[J].湖南人文科技学院学报,2011(2)：71-73.

更新日期/Last Update: 2015-08-25