On the Role of Sparsity in Compressed Sensing and Random Matrix Theory

Details On the Role of Sparsity in Compressed Sensing and Random Matrix Theory On the Role of Sparsity in Compressed Sensing and Random Matrix Theory

2009-08-03

arxiv.org/abs/0908.0257v1

Mathematics

Numerical Analysis

4 pages

Scientific paper

We discuss applications of some concepts of Compressed Sensing in the recent
work on invertibility of random matrices due to Rudelson and the author. We
sketch an argument leading to the optimal bound N^{-1/2} on the median of the
smallest singular value of an N by N matrix with random independent entries. We
highlight the parts of the argument where sparsity ideas played a key role.

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