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Large deviations of the largest and smallest eigenvalues of 
$\mathbf{X}\mathbf{X}^\top/n$ are studied in this note, where 
$\mathbf{X}_{p\times n}$ is a 
$p\times n$ random matrix with independent and identically distributed (i.i.d.) sub-Gaussian entries. The assumption imposed on the dimension size p and the sample size n is 
$p=p(n)\rightarrow\infty$ with 
$p(n)={\mathrm{o}}(n)$. This study generalizes one result obtained in [3].
