most recent 30 from http://mathoverflow.net 2013-05-19T08:52:29Z http://mathoverflow.net/feeds/question/103880 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/103880/when-is-the-inverse-diagonally-dominant Felix Goldberg 2012-08-03T16:20:10Z 2012-09-06T14:19:31Z

<p>There is a large literature devoted to studying the inverses of diagonally dominant matrices. I'd like to know if there is information about a so-to-say opposite situation: we have a matrix $A$ and want to find conditions under which $A^{-1}$ will be diagonally dominant. </p> <p>One case which has been studied is that of strictly ultrametric matrices whose inverses are known to be Stieltjes matrices. But what if the original matrix has some negative entries?</p> <p>UPDT: References to two papers, as requested some time ago:</p> <p>(1) Li, Yaotang; Liu, Xin; Yang, Xiaoying; Li, Chaoqian Some new lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse. (English) [J] Electron. J. Linear Algebra 22, 630-643, electronic only (2011).</p> <p>(2) Ostrowski, A.M. Note on bounds for determinants with dominant principal diagonal. (English) [J] Proc. Am. Math. Soc. 3, 26-30 (1952).</p>