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 $(c_{nr})$.

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

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