# 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

Abstract: 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].

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