COMPANION MATRICES ASSOCIATED TO STOCHASTIC MATRICES

Authors

• Andreas Boukas, Centro Vito Volterra and Hellenic Open University, Graduate School of Mathematics, GreeceFollow
• Philip Feinsilver, Southern Illinois University CarbondaleFollow

Abstract

Starting with a stochastic matrix, we study the behavior of powers of an associated companion matrix, which has the same characteristic polynomial as the original matrix. In general the companion matrix will have negative entries while maintaining rowsums equal to 1. We will find the growth rate even if the Ces`aro limit of the sums of the companion matrix diverge. Surprisingly, in the irreducible aperiodic case the powers of the companion matrix will converge even though the norm of the matrix exceeds 1 and it has possibly negative entries.

Recommended Citation

Boukas, Andreas and Feinsilver, Philip (2026) "COMPANION MATRICES ASSOCIATED TO STOCHASTIC MATRICES," Journal of Stochastic Analysis: Vol. 7: No. 3, Article 2.
DOI: 10.31390/josa.7.3.02
Available at: https://repository.lsu.edu/josa/vol7/iss3/2

DOI

10.31390/josa.7.3.02