Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The generalized numerical range of a set of matrices   For a given set of $n\times n$ matrices $\mathcal F$, we study the union of
the $C$-numerical ranges of the matrices in the set $\mathcal F$, denoted by
$W_C({\mathcal F})$. We obtain basic algebraic and topological properties of
$W_C({\mathcal F})$, and show that there are connections between the geometric
properties of $W_C({\mathcal F})$ and the algebraic properties of $C$ and the
matrices in ${\mathcal F}$. Furthermore, we consider the starshapedness and
convexity of the set $W_C({\mathcal F})$. In particular, we show that if
${\mathcal F}$ is the convex hull of two matrices such that $W_C(A)$ and
$W_C(B)$ are convex, then the set $W_C({\mathcal F})$ is star-shaped. We also
investigate the extensions of the results to the joint $C$-numerical range of
an $m$-tuple of matrices.

8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph