Estimates for eigenvalues of stochastic matrices |
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| Authors: | Jia-li Zhou Min Wu Shu-you Zhang Guo-ping Yang |
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| Institution: | Jia-li Zhou 1,2,Min Wu 3,Shu-you Zhang 2,Guo-ping Yang 4 1 Department of Mathematics,Zhejiang University of Technology,Zhejiang 310023,China2 State Key Lab of CAD & CG,Zhejiang University,Zhejiang 310027,China 3 Department of Mathematics,Zhejiang University of Science & Technology,China 4 College of Information Technology,Zhejiang Chinese Medical University,Zhejiang 310053,China |
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| Abstract: | It is well-known that the eigenvalues of stochastic matrices lie in the unit circle and at least one of them has the value
one. Let {1, r
2, …, r
N
} be the eigenvalues of stochastic matrix X of size N × N. We will present in this paper a simple necessary and sufficient condition for X such that |r
j
| < 1, j = 2, …, N. Moreover, such condition can be very quickly examined by using some search algorithms from graph theory. |
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| Keywords: | Directed graph eigenvalues spectral radius stochastic matrix |
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