Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resistance matrices of graphs with matrix weights   The \emph{resistance matrix} of a simple connected graph $G$ is denoted by
$R$, and is defined by $R =(r_{ij})$, where $r_{ij}$ is the resistance distance
between the vertices $i$ and $j$ of $G$. In this paper, we consider the
resistance matrix of weighted graph with edge weights being positive definite
matrices of same size. We derive a formula for the determinant and the inverse
of the resistance matrix. Then, we establish an interlacing inequality for the
eigenvalues of resistance and Laplacian matrices. Using this interlacing
inequality, we obtain the inertia of the resistance matrix.

21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics