Companion unit lower Hessenberg matrices

Alberto Borobia; Roberto Canogar

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arXiv · 2001.06470

Companion unit lower Hessenberg matrices

Alberto Borobia·Roberto Canogar

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Abstract

In recent years there has been a growing interest in companion matrices. There is a deep knowledge of sparse companion matrices, in particular it is known that every sparse companion matrix can be transformed into a unit lower Hessenberg matrix of a particularly simple type by any combination of transposition, permutation similarity and diagonal similarity. The latter is not true for the companion matrices that are non-sparse, although it is known that every non-sparse companion matrix is nonderogatory. In this work the non-sparse companion matrices that are unit lower Hessenberg will be described. A natural generalization is also considered.

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Alberto Borobia, Roberto Canogar. 2020-01-17. Companion unit lower Hessenberg matrices. https://arxiv.org/abs/2001.06470

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