The condition number of a randomly perturbed matrix

Details The condition number of a randomly perturbed matrix The condition number of a randomly perturbed matrix

2007-03-11

arxiv.org/abs/math/0703307v1

Mathematics

Probability

8 pages, no figures, to appear, STOC '07

Scientific paper

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.

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