# A Remark on Matrix Rigidity

**Authors:**
M. Amin Shokrollahi,
Daniel Spielman,
and Voelker Stemann.
**Bibliographic Information:**
*Information Processing Letters,*
64(6), pp. 283--285, December 1997.

## Abstract

The rigidity of a matrix is defined to be the number of entries in the
matrix that have to be changed in order to reduce its rank below a
certain value. Using a simple combinatorial lemma, we show that one
must alter at least $c\frac{n^2}{r}\log\frac{n}{r}$ entries of an
$n\times n$-Cauchy matrix to reduce its rank below $r$, for some
constant $c$. In the second
part of the paper we apply our combinatorial lemma to matrices
obtained from asymptotically good algebraic geometric codes to obtain
a similar result for $r$ satisfying $2n/(\sqrt{q}-1)

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