A canonical form for nonderogatory matrices under unitary similarity

Details A canonical form for nonderogatory matrices under unitary similarity A canonical form for nonderogatory matrices under unitary similarity

2011-12-15

arxiv.org/abs/1112.3682v1

Linear Algebra and its Applications 435 (2011) 830-841

Mathematics

Representation Theory

18 pages

Scientific paper

10.1016/j.laa.2011.01.042

A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms (i) for nonderogatory complex matrices up to unitary similarity and (ii) for 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.

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