Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An improved bound for the length of matrix algebras   Let $S$ be a set of $n\times n$ matrices over a field $\mathbb{F}$. We show
that the $\mathbb{F}$-linear span of the words in $S$ of length at most
$$2n\log_2n+4n$$ is the full $\mathbb{F}$-algebra generated by $S$. This
improves on the $n^2/3+2/3$ bound by Paz (1984) and an $O\left(n^{1.5}\right)$
bound of Pappacena (1997).

9
The categories of this paper are: nlin
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess