Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On eigenvalue and eigenvector estimates for nonnegative definite
  operators   In this article we further develop a perturbation approach to the
Rayleigh--Ritz approximations from our earlier work. We both sharpen the
estimates and extend the applicability of the theory to nonnegative definite
operators . The perturbation argument enables us to solve two problems in one
go: We determine which part of the spectrum of the operator is being
approximated by the Ritz values and compute the approximation estimates. We
also present a Temple--Kato like inequality which --unlike the original
Temple--Kato inequality-- applies to any test vectors from the quadratic form
domain of the operator.

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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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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: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg