Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive definite matrices in the view-points of planar networks and
  cluster subalgebras   As an improvement of the combinatorial realization of totally positive
matrices via the essential positive weightings of certain planar network by
  S.Fomin and A.Zelevisky \cite{[4]}, in this paper, we give the test method of
positive definite matrices via the planar networks and the so-called cluster
subalgebra respectively, introduced here originally.
  This work firstly gives a combinatorial realization of all matrices through
planar network, and then sets up a test method for positive definite matrices
by $LDU$-decompositions and the horizontal weightings of all lines in their
planar networks. On the other hand, mainly the relationship is built between
positive definite matrices and cluster subalgebras.

36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con