Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The condition number of a randomly perturbed matrix   Let $M$ be an arbitrary $n$ by $n$ matrix. We study the condition number a
random perturbation $M+N_n$ of $M$, where $N_n$ is a random matrix. It is shown
that, under very general conditions on $M$ and $M_n$, the condition number of
$M+N_n$ is polynomial in $n$ with very high probability. The main novelty here
is that we allow $N_n$ to have discrete distribution.

36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat