Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Companion unit lower Hessenberg matrices   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.

10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg