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Positivity and matrix semigroups |
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| Authors: | Janez Bernik Mitja Mastnak |
| Institution: | a Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia b Department of Mathematics and Computer Science, Saint Marys University, Halifax, Nova Scotia, Canada B3H 3C3 c Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 |
| Abstract: | We study various aspects of how certain positivity assumptions on complex matrix semigroups affect their structure. Our main result is that every irreducible group of complex matrices with nonnegative diagonal entries is simultaneously similar to a group of weighted permutations. We also consider the corresponding question for semigroups and discuss the effect of the assumption that a fixed linear functional has nonnegative values when restricted to a given semigroup. |
| Keywords: | 15A30 15A48 20M20 47D03 |
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