Norm bound of the entrywise logarithm of a stochastic matrix stationary matrix - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T05:20:42Z http://mathoverflow.net/feeds/question/111940 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111940/norm-bound-of-the-entrywise-logarithm-of-a-stochastic-matrix-stationary-matrix Norm bound of the entrywise logarithm of a stochastic matrix stationary matrix Daniel86 2012-11-09T21:11:24Z 2012-11-10T11:07:40Z <p>Hello,</p> <p>Denote $\log_\star$ as the entrywise logarithm operation, and let $A$ be some row-stochastic matrix such that $\lim_{p\rightarrow\infty}A^p$ exists and all its entries are non-zero.</p> <p>As a part of my research, I am interested in upper-bounding the following expression: $\parallel\log_\star \lim_{p\rightarrow\infty}A^p\parallel_2$, in terms of $\parallel A\parallel_2$. </p> <p>Does anyone have an idea?</p> <p>Thank you.</p>