# Could someone help me to prove or disprove the following inequality?

Let $$(c_{nr})$$ be an $$Ntimes R$$ complex matrix, then $$forall z_n in mathbb{C}$$, we have
$$sum_r |sum_n c_{nr}z_n|^2 geq frac{1}{sigma_{max}} sum_n |z_n|^2$$
where $$sigma_{max}$$ is the maximal sigular value of the complex matrix $$(c_{nr})$$.