Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The spectral norm error of the naive Nystrom extension   The naive Nystrom extension forms a low-rank approximation to a
positive-semidefinite matrix by uniformly randomly sampling from its columns.
This paper provides the first relative-error bound on the spectral norm error
incurred in this process. This bound follows from a natural connection between
the Nystrom extension and the column subset selection problem. The main tool is
a matrix Chernoff bound for sampling without replacement.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph