%0 Journal Article %T Matrix sparsification and the sparse null space problem %A Lee-Ad Gottlieb %A Tyler Neylon %J Mathematics %D 2010 %I arXiv %X We revisit the matrix problems sparse null space and matrix sparsification, and show that they are equivalent. We then proceed to seek algorithms for these problems: We prove the hardness of approximation of these problems, and also give a powerful tool to extend algorithms and heuristics for sparse approximation theory to these problems. %U http://arxiv.org/abs/1008.1498v1