Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pairs of $k$-step reachability and $m$-step observability matrices   Let $V$ and $W$ be matrices of size $ n \times pk$ and $q m \times n $,
respectively. A necessary and sufficient condition is given for the existence
of a triple $(A,B,C)$ such that $V$ a $k$-step reachability matrix of $(A,B)$
and $W$ an $m$-step observability matrix of $(A,C)$.

36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics