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Regular stochastic matrices and digraphs

Published online by Cambridge University Press:  14 July 2016

Elizabeth Berman
Elizabeth Berman*
Affiliation:
Rockhurst College, Kansas City, Missouri
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Abstract

This paper presents an algorithm to determine whether a stochastic matrix is regular. The main theorem is the following. Hypothesis: An n-by-n stochastic matrix has at least one positive entry off the main diagonal in every row and column. There is at most one row with n — 1 zeros and at most one column with n — 1 zeros. There are no j-by-k submatrices consisting entirely of zeros, where j and k are integers greater than 1, with j + k = n. Conclusion: The matrix is regular. Similar results hold for strongly connected digraphs.

Keywords

REGULAR STOCHASTIC MATRICESERGODIC MARKOV CHAINSSTRONGLY CONNECTED DIGRAPHS
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 241 - 243
Copyright
Copyright © Applied Probability Trust 1973 

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