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A canonical form for nonderogatory matrices under unitary similarity

Authors:	Vyacheslav Futorny Roger A Horn

Institution:	^a Department of Mathematics, University of São Paulo, Brazil ^b Department of Mathematics, University of Utah, Salt Lake City, UT 84103, USA ^c Institute of Mathematics, Tereshchenkivska 3, Kiev, Ukraine

Abstract:	A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for • nonderogatory complex matrices up to unitary similarity, and • pairs of complex matrices up to similarity, in which one matrix has distinct eigenvalues. The types of these canonical forms are given by undirected and, respectively, directed graphs with no undirected cycles.

Keywords:	15A21
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