Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algorithms and Properties for Positive Symmetrizable Matrices   Matrices are the most common representations of graphs. They are also used
for the representation of algebras and cluster algebras. This paper shows some
properties of matrices in order to facilitate the understanding and locating
symmetrizable matrices with specific characteristics, called positive
quasi-Cartan companion matrices. Here, symmetrizable matrix are those which are
symmetric when multiplied by a diagonal matrix with positive entries called
symmetrizer matrix. Four algorithms are developed: one to decide whether there
is a symmetrizer matrix; second to find such symmetrizer matrix; another to
decide whether the matrix is positive or not; and the last to find a positive
quasi-Cartan companion matrix, if there exists. The third algorithm is used to
prove that the problem to decide if a matrix has a positive quasi-Cartan
companion is NP.

15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
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The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg