Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on the Spectral Sparsification of Symmetric and Off-Diagonal
  Nonnegative Real Matrices   We say that a square real matrix $M$ is \emph{off-diagonal nonnegative} if
and only if all entries outside its diagonal are nonnegative real numbers. In
this note we show that for any off-diagonal nonnegative symmetric matrix $M$,
there exists a nonnegative symmetric matrix $\widehat{M}$ which is sparse and
close in spectrum to $M$.

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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex