= Null space property
{wiki=Nullspace_property}
= Nullspace property
{synonym}
The null space property relative to $S$ is $\|h_S\|_1<\|h_{S^c}\|_1$ for every nonzero $h\in\ker A$. It is equivalent to exact <basis pursuit> recovery of every vector supported in $S$. Sufficiency follows from the <triangle inequality>; for necessity, compare $-h_S$ and $h_{S^c}$, which have the same image under $A$. Recovery of a single fixed signed vector can hold without this uniform property.
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