  This paper investigates an upper bound of the operator norm for sub-Gaussian
tailed random matrices. A lot of attention has been put on uniformly bounded
sub-Gaussian tailed random matrices with independent coefficients. However,
little has been done for sub-Gaussian tailed random matrices whose matrix
coefficients variance are not equal or for matrix for which coefficients are
not independent. This is precisely the subject of this paper. After proving
that random matrices with uniform sub-Gaussian tailed independent coefficients
satisfy the Tracy Widom bound, that is, their matrix operator norm remains
bounded by $O(\sqrt n )$ with overwhelming probability, we prove that a less
stringent condition is that the matrix rows are independent and uniformly
sub-Gaussian. This does not impose in particular that all matrix coefficients
are independent, but only their rows, which is a weaker condition.
