# Ranks of linear matrix pencils separate simultaneous similarity orbits

@inproceedings{Derksen2021RanksOL, title={Ranks of linear matrix pencils separate simultaneous similarity orbits}, author={Harm Derksen and Igor Klep and Visu Makam and Jurij Volvcivc}, year={2021} }

Abstract. This paper solves the two-sided version and provides a counterexample to the general version of the 2003 conjecture by Hadwin and Larson. Consider evaluations of linear matrix pencils L = T0 + x1T1 + · · · + xmTm on matrix tuples as L(X1, . . . , Xm) = I ⊗ T0 + X1 ⊗ T1 + · · · + Xm ⊗ Tm. It is shown that ranks of linear matrix pencils constitute a collection of separating invariants for simultaneous similarity of matrix tuples. That is, m-tuples A and B of n × n matrices are… Expand

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