I am reading Tao's Random matrix notes, specifically Proof of Corollary 2.3.5.
Corollary 2.3.5. (Upper tail estimate for iid ensembles). Suppose that the coefficients $\sigma_{ij}$ of $M$ are independent, have mean zero, and uniformly bounded in magnitude by $1$. Then there exists absolute constants $C,c>0$ such that $$P(\|M\|_{op}>A\sqrt{n}\leq C\exp(-cAn)$$ for all $A\geq C$.
In the proof, I understand that $P(\|M\|_{op}>A\sqrt{n})\leq\sum_{y\in\sum}P(|My|>A\sqrt{n}/2)$. And then, how to choose $A$ and $c$ explicitly, such that the bound can be written as $C\exp(-cAn)$. This is not clearly written in the proof. Could someone help me out?
Thanks!