If $m\times n~(m<n)$ matrix $A$ satisfy the following condition $(1-\delta)||s||_2^2\leqslant \|As\|^2_2\leqslant (1+\delta)\|s\|_2^2$ for all the $n \times 1$ vector with no more than $k$ nonzero entries, we call $A$ satisfy the $k$-th RIP condition.
Multiple $A$ by a $n \times n$ matrix at the right, we get $AB$, will $AB$ still satisfy the $k$-th RIP condition? If not, anyone can give me a counterexample? tks a lot.