Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounded Ratios of Products of Principal Minors of Positive Definite
  Matrices   Considered is the multiplicative semigroup of ratios of products of principal
minors bounded over all positive definite matrices. A long history of
literature identifies various elements of this semigroup, all of which lie in a
sub-semigroup generated by Hadamard-Fischer inequalities. Via cone-theoretic
techniques and the patterns of nullity among positive semidefinite matrices, a
semigroup containing all bounded ratios is given. This allows the complete
determination of the semigroup of bounded ratios for 4-by-4 positive definite
matrices, whose 46 generators include ratios not implied by Hadamard-Fischer
and ratios not bounded by 1. For n > 4 it is shown that the containment of
semigroups is strict, but a generalization of nullity patterns, of which one
example is given, is conjectured to provide a finite determination of all
bounded ratios.

26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat