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.Acta et Commentationes Universitatis Tartuensis de Mathematica is an open access journal starting with volume 14 (2010). This means that all content is freely available without charge on the website of the journal (http://www.math.ut.ee/acta/). Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author.Markov chainsStochastic matricesColumn sumsStationary distributionsMean rst passage timesKemeny constantGeneralized matrix inversesJournal ArticleOpenAccess