Abstract:Let Bn (resp. Un, Nn) be the set of n × n nonsingular (resp. unit, nilpotent) upper triangular matrices. We use a novel approach to explore the Bn-similarity orbits in Nn. The Belitskiȋ's canonical form of A ∈ Nn under Bn-similarity is in QUn where Q is the subpermutation such that A ∈ BnQBn. Using graph representations and Un-similarity actions stabilzing QUn, we obtain new properties of the Belitskiȋ's canonical forms and present an efficient algorithm to find the Belitskiȋ's canonical forms in Nn. As conseq… Show more
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