Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical radius and zero pattern of matrices   We give tight upper bounds on the numerical range of square matrices in terms
of their Frobenius (Euclidian) norm and a combinatorial parameter similar to
the clique number of graphs. Our results imply a concise form of the
fundamental theorem of Turan in extremal graph theory.

30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio