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The sparsity problems have attracted a great deal of attention in recent years, which aim to find the sparsest solution of a representation or an equation. In the paper, we mainly study the sparsity of underdetermined linear system vialpminimization for0<p<1. We show, for a given underdetermined linear system of equationsAm×nX=b, that although it is not certain that the problem(Pp)(i.e.,minXXppsubject toAX=b, where0<p<1) generates sparser solutions as the value ofpdecreases and especially thedoi:10.1155/2015/584712 fatcat:wmg2a77xnzh65hg5xtq65ksteu