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Ranks of linear matrix pencils separate simultaneous similarity orbits
Derksen, Harm ...
Članek reši dvostransko različico in predstavi protiprimer splošne različice domneve Hadwina in Larsona iz leta 2003. Vrednotenja linearnih matričnih šopov ▫$L=T_0+x_1T_1+\cdots+x_mT_m$▫ na matričnih ...▫$m$▫-tericah so definirana kot ▫$L(X_1,\dots,X_m)=I\otimes T_0+X_1\otimes T_1+\cdots+X_m\otimes T_m$▫. Pokazano je, da linearni matrični šopi določajo separirajoče invariante za simultano podobnost matričnih dvojic. To pomeni, da sta si ▫$m$▫-terici ▫$A$▫ in ▫$B$▫ ▫$n\times n$▫ matrik simultano podobni takrat in samo takrat, ko sta ranga ▫$L(A)$▫ in ▫$L(B)$▫ enaka za vse linearne matrične šope ▫$L$▫ velikosti ▫$mn$▫.
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