A note on the coefficient of ergodicity of a column-allowable nonnegative matrix (Q1345503)

The (Birkhoff) coefficient of ergodicity \(\tau_ B (T)\) for an \(n \times n\) nonnegative matrix \(T\) with no zero columns is given in explicit form. The derivation is simpler than in the reviewer's book [Non-negative matrices and Markov chains (1981; Zbl 0471.60001)]. At the same time a simple connection is displayed between \(\tau_ B (T)\) and the Markov- Dobrushin coefficient of ergodicity of a row stochastic matrix closely related to \(T\). This last generalizes another result (p. 110) in the book.