Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of nonnegativity relative to proper cones   Let $A$ be an $m \times n$ matrix with real entries. Given two proper cones
$K_1$ and $K_2$ in $\mathbb{R}^n$ and $\mathbb{R}^m$, respectively, we say that
$A$ is nonnegative if $A(K_1) \subseteq K_2$. $A$ is said to be semipositive if
there exists a $x \in K_1^\circ$ such that $Ax \in K_2^\circ$. We prove that
$A$ is nonnegative if and only if $A+B$ is semipositive for every semipositive
matrix $B$. Applications of the above result are also brought out.

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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg