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A canonical form for nonderogatory matrices under unitary similarity

✍ Scribed by Vyacheslav Futorny; Roger A. Horn; Vladimir V. Sergeichuk

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
241 KB
Volume
435
Category
Article
ISSN
0024-3795

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✦ Synopsis

A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for (1) nonderogatory complex matrices up to unitary similarity, and (2) 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.

πŸ“œ SIMILAR VOLUMES

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✍ Douglas Farenick; Vyacheslav Futorny; Tatiana G. Gerasimova; Vladimir V. Sergeic πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 269 KB

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A = [a ij ] and B = [b ij ] be upper triangular n Γ— n matrices that β€’ are not similar to direct sums of square matrices of smaller sizes, or β€’ are in general position an

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In this paper we give necessary and sufficient conditions for a matrix in Jordan canonical form to be similar to an eventually nonnegative matrix whose irreducible diagonal blocks satisfy the conditions identified by Zaslavsky and Tam, and whose subdiagonal blocks (with respect to its Frobenius norm