The Estimation for the Eigenvalues of Stochastic Matrices
نویسنده
چکیده
In the past two decades, due to study on matrix theory and some engineering background problems, many scholars dedicated to special matrix , and obtained some important and valuable results (TingZhu, 2007 Yigeng Huang, 1994). But in combination matrix theory, combinatorics, probability theory (especially Markov chain), mathematical economics and reliability theory etc. areas there is a special class of non-negative stochastic matrix, which in recent years becomes concerned. This article discusses location, distribution and estimate of the eigenvalue for stochastic matrix . Section 2 introduces the concepts of stochastic matrix and generalized stochastic matrix. Section 3 gives a few estimation theorems of stochastic matrix eigenvalue, also the eigenvalue distribution for tensor product of two stochastic matrices is obtained. In section 4, we discuss the eigenvalue distribution for generalized stochastic matrices.
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