 Restricted isometry constant

The order-s restricted isometry constant is the smallest nonnegative $\delta$ satisfying $(1-\delta )\Vert x{\Vert }_2^2\le \Vert Ax{\Vert }_2^2\le (1+\delta )\Vert x{\Vert }_2^2$ for every vector with at most $s$ nonzero coordinates. Equivalently it is ${\max }_{|S|\le s}\Vert A_S^{\ast }{A}_S-I{\Vert }_{2\to 2}$. The sparse-vector quantifier is essential, and the constant can equal zero.