Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-scalar equivalence of polynomial matrices   Polynomial $n\times n$ matrices $A(\lambda)$ and $B(\lambda)$ over a field
$\mathbb F $ are called semi-scalar equivalent if there exist a nonsingular
$n\times n$ matrix $P$ over the field $\mathbb F $ and an invertible $n\times
n$ matrix $Q(\lambda)$ over the ring ${\mathbb F}[\lambda]$ such that
$A(\lambda)=P B(\lambda)Q(\lambda).$ The semi-scalar equivalence of matrices
over a field $ {\mathbb F} $ contain the problem of similarity between two
families of matrices. Therefore, these equivalences of matrices can be
considered a difficult problem in linear algebra.
  The aim of the present paper is to present the necessary and sufficient
conditions of semi-scalar equivalence of nonsingular matrices $A(\lambda)$ and
$ B(\lambda) $ over a field ${\mathbb F }$ of characteristic zero in terms of
solutions of a homogenous system of linear equations. We also establish
similarity of monic polynomial matrices $A(\lambda)$ and $B(\lambda)$ over a
field.

13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an