2020/01/17 by Alberto Borobia, Borobia, Alberto, Roberto Canogar +1
Computer Science · Engineering · Mathematics · #15A21 #15A54 #15B99 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #Spectral Theory (math.SP) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2001.06470
openalex publication_date 2020/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.