Hunter, JJ2012-12-042013-01-102013-01-102012-12-042013-01-102013-01-1020122012Acta et Commentationes Universitatis Tartuensis de Mathematica, vol.16(1), pp.33 - 51 (29)1406-2283https://hdl.handle.net/10292/4981Questions are posed regarding the influence that the column sums of the transition probabilities of a stochastic matrix (with row sums all one) have on the stationary distribution, the mean first passage times and the Kemeny constant of the associated irreducible discrete time Markov chain. Some new relationships, including some inequalities, and partial answers to the questions, are given using a special generalized matrix inverse that has not previously been considered in the literature on Markov chains.This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. All papers are published under CC BY-NC-ND licence. Authors retain copyright without restrictions. This journal does not have article processing or submission charges.Markov chainsStochastic matricesColumn sumsStationary distributionsMean rst passage timesKemeny constantGeneralized matrix inversesJournal ArticleOpenAccess10.12697/ACUTM.2012.16.03