理论数学

Vol.5 No.5 (September 2015)

随机矩阵新的非1特征值包含集
New Sets to Localize All Eigenvalues Different from 1 for a Stochastic Matrix

 

作者:

李素华 , 李耀堂 :云南大学,数学与统计学院,云南 昆明

 

关键词:

随机矩阵S-SDD矩阵具有相同行和实矩阵非奇异特征值包含集Stochastic Matrices S-SDD Matrices Real Matrices with Same Row Sums Nonsingular Eigenvalue Inclusion Set

 

摘要:

本文利用S-SDD矩阵的非奇异性及修正矩阵理论,给出具有非零相同行和实矩阵非奇异的三个新的充分条件,进而得到了随机矩阵的三个新的非1特征值包含集。数值例子表明,所得结果改进了Shen et al. [Linear Algebra Appl., 447 (2014) 74-87],Cvetkovic et al. [ETNA., 18 (2004) 73-80]和Li et al. [Linear and Multilinear Algebra, http://dx.doi.org/10.1080/03081087.2014.986044]的结果。

By using the nonsingularity of S-SDD matrices and the theory of modified matrices, three new suf-ficient conditions of the nonsingular real matrices with nonzero same row sums are given, and then three new sets to localize all eigenvalues different from 1 for a stochastic matrix are obtained. Numerical examples are given to illustrate that the proposed results are better than the results of Shen et al. [Linear Algebra Appl., 447(2014)74-87], Cvetkovic et al. [ETNA., 18(2004)73-80] and Li et al. [Linear and Multilinear Algebra, http://dx.doi.org/10.1080/03081087.2014.986044].

文章引用:

李素华 , 李耀堂 (2015) 随机矩阵新的非1特征值包含集。 理论数学, 5, 238-246. doi: 10.12677/PM.2015.55034

 

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