Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unique "Nonnegative" Solution to an Underdetermined System: from
  Vectors to Matrices   This paper investigates the uniqueness of a nonnegative vector solution and
the uniqueness of a positive semidefinite matrix solution to underdetermined
linear systems. A vector solution is the unique solution to an underdetermined
linear system only if the measurement matrix has a row-span intersecting the
positive orthant. Focusing on two types of binary measurement matrices,
Bernoulli 0-1 matrices and adjacency matrices of general expander graphs, we
show that, in both cases, the support size of a unique nonnegative solution can
grow linearly, namely O(n), with the problem dimension n. We also provide
closed-form characterizations of the ratio of this support size to the signal
dimension. For the matrix case, we show that under a necessary and sufficient
condition for the linear compressed observations operator, there will be a
unique positive semidefinite matrix solution to the compressed linear
observations. We further show that a randomly generated Gaussian linear
compressed observations operator will satisfy this condition with
overwhelmingly high probability.

17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th