Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitely divisible nonnegative matrices, $M$-matrices, and the
  embedding problem for finite state stationary Markov Chains   This paper explicitly details the relation between $M$-matrices, nonnegative
roots of nonnegative matrices, and the embedding problem for finite-state
stationary Markov chains. The set of nonsingular nonnegative matrices with
arbitrary nonnegative roots is shown to be the closure of the set of matrices
with matrix roots in $\mathcal{IM}$. The methods presented here employ nothing
beyond basic matrix analysis, however it answers a question regarding
$M$-matrices posed over 30 years ago and as an application, a new
characterization of the set of all embeddable stochastic matrices is obtained
as a corollary.

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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph