Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linearizations of rational matrices from general representations   We construct a new family of linearizations of rational matrices $R(\lambda)$
written in the general form $R(\lambda)=
D(\lambda)+C(\lambda)A(\lambda)^{-1}B(\lambda)$, where $D(\lambda)$,
$C(\lambda)$, $B(\lambda)$ and $A(\lambda)$ are polynomial matrices. Such
representation always exists and are not unique. The new linearizations are
constructed from linearizations of the polynomial matrices $D(\lambda)$ and
$A(\lambda)$, where each of them can be represented in terms of any polynomial
basis. In addition, we show how to recover eigenvectors, when $R(\lambda)$ is
regular, and minimal bases and minimal indices, when $R(\lambda)$ is singular,
from those of their linearizations in this family.

36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin