PM  >> Vol. 6 No. 4 (July 2016)

    The New Inclusion Region of Eigenvalue Different from 1 for a Stochastic Matrix

  • 全文下载: PDF(2129KB) HTML   XML   PP.361-367   DOI: 10.12677/PM.2016.64051  
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周宝星,李耀堂:云南大学,数学与统计学院,云南 昆明;
卫慧芳:云南财经大学,统计与数学学院,云南 昆明

随机矩阵α1-矩阵非1特征值 α-型特征值包含定理Stochastic Matrices α1-Matrices Eigenvalue Different from 1 α-Eigenvalue Inclusion Theorem



Two new inclusion regions of eigenvalue different from 1 of stochastic matrices are given by using the -eigenvalue inclusion theorem and the theory of modified matrices; and two new sufficient conditions of stochastic matrices nonsingular are obtained. Numerical examples are given to show that the existing results are improved in some cases.

周宝星, 卫慧芳, 李耀堂. 随机矩阵非1特征值的新包含区域[J]. 理论数学, 2016, 6(4): 361-367.


[1] Horn, R.A. and Johnson, C.R. (1986) Matrix Analysis. Cambridge University Press, Cambridge, England.
[2] Seneta, E. (2004) Nonnegative Matrices and Markov Chains. Springer-Verlag, Berlin.
[3] Cvetković, L., Kostic, V. and Pena, J.M. (2011) Eigenvalue Localization Refinements for Matrices Related to Positivity. SIAM Journal on Matrix Analysis and Applications, 32, 771-784.
[4] Varga, R.S. (2004) Gersgorin and His Circles. Springer-Verlag, Berlin.
[5] Cvetkovic, L., Kostic, V. and Varga, R.S. (2004) A New Gersgorin-Type Eigenvalue Inclusion Set. Electronic Transactions on Numerical Analysis, 18, 73-80.
[6] Shen, S.Q., Yu, J. and Huang, T.Z. (2014) Some Classes of Nonsingular Matrices with Applications to Localize the Real Eigenvalues of Real Matrices. Linear Algebra and Its Applications, 447, 74-87.
[7] Li, C.Q., Liu, Q.B. and Li, Y.T. (2014) Gersgorin-Type and Brauer-Type Eigenvalue Localization Sets of Stochastic Matrices. Linear and Multilinear Algebra.
[8] Cvetković, L. (2007) H-Matrix Theory vs. Eigenvalue Localization. Numerical Algorithms, 42, 229-245.