摘要
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.
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.
基金
Supported by grants from Science & Technology Pillar Program of Zhejiang Province (No. 2008C21084, No. 2009C31120, No. 2009C34006)
Key Industrial Projects of Major Science & Technology Projects of Zhejiang Province (No. 2009C11023)
Foundation of Zhejiang Educational Committee (No. Y200804427)
