# Matrix rigidity and the Croot-Lev-Pach lemma

@article{Dvir2017MatrixRA, title={Matrix rigidity and the Croot-Lev-Pach lemma}, author={Zeev Dvir and Benjamin Edelman}, journal={ArXiv}, year={2017}, volume={abs/1708.01646} }

Matrix rigidity is a notion put forth by Valiant as a means for proving arithmetic circuit lower bounds. A matrix is rigid if it is far, in Hamming distance, from any low rank matrix. Despite decades of efforts, no explicit matrix rigid enough to carry out Valiant's plan has been found. Recently, Alman and Williams showed, contrary to common belief, that the $2^n \times 2^n$ Hadamard matrix could not be used for Valiant's program as it is not sufficiently rigid. In this note we observe a… CONTINUE READING

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