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Given linear matrix inequalities (LMIs) L1 and L2 in the same number of variables it is natural to ask: (Q1) 1) does one dominate the other, that is, does L1(X) 0 imply L2(X) 0? 2) are they mutually dominant, that is, do they have the same solution set? Such problems can be NP-hard. We describe a natural relaxation of an LMI, based on substituting matrices for the variables xj. With this relaxation, the domination questions (Q1) and (Q2) have elegant answers, indeed reduce to semidefinitedoi:10.1109/cdc.2010.5717737 dblp:conf/cdc/HeltonKM10 fatcat:whig4wogh5aa3dv22owifgmspa