  Motivated by the general matrix deviation inequality for i.i.d ensemble
Gaussian matrix, we study its universality property. As a starting point for
this problem, we show that this property holds for $\ell_{p}$-norm with $1\leq
p< \infty$ and i.i.d ensemble sub-Gaussian random matrix, which is a random
matrix with i.i.d mean-zero, unit variance, sub-Gaussian entries.
