标题:
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
关键字:
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
期刊名称:
《Pure Mathematics》, Vol.5 No.5, 2015-09-28
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].