A SPECTRAL CHARACTERIZATION OF STOCHASTIC MATRICES.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Let A be an vector product of n an n matrix over a field F with identity element 1. The matrix A is called row column stochastic if all row column sums of A equal 1. The following characterization is obtained A is row or column stochastic if and only if 1 is a characteristic root of PA for all vector product of n an n permutation matrices P. The problem is then varied and all matrices A are determined for which the spectrum of A is the same as the spectrum of PA for all vector product of n an n permutation matrices P. In case the characteristic of F is either 0 or relatively prime to n, the description is very simple either all row vectors or all column vectors are identical. Author
- Statistics and Probability