Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved Bounds on Restricted Isometry Constants for Gaussian Matrices   The Restricted Isometry Constants (RIC) of a matrix $A$ measures how close to
an isometry is the action of $A$ on vectors with few nonzero entries, measured
in the $\ell^2$ norm. Specifically, the upper and lower RIC of a matrix $A$ of
size $n\times N$ is the maximum and the minimum deviation from unity (one) of
the largest and smallest, respectively, square of singular values of all
${N\choose k}$ matrices formed by taking $k$ columns from $A$. Calculation of
the RIC is intractable for most matrices due to its combinatorial nature;
however, many random matrices typically have bounded RIC in some range of
problem sizes $(k,n,N)$. We provide the best known bound on the RIC for
Gaussian matrices, which is also the smallest known bound on the RIC for any
large rectangular matrix. Improvements over prior bounds are achieved by
exploiting similarity of singular values for matrices which share a substantial
number of columns.

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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org