  In this paper, we shall investigate the almost sure limits of the largest and
smallest eigenvalues of a quaternion sample covariance matrix. Suppose that
$\mathbf X_n$ is a $p\times n$ matrix whose elements are independent quaternion
variables with mean zero, variance 1 and uniformly bounded fourth moments.
Denote $\mathbf S_n=\frac{1}{n}\mathbf X_n\mathbf X_n^*$. In this paper, we
shall show that $s_{\max}\left(\mathbf S_n\right)=s_{p}\left(\mathbf
S_n\right)\to\left(1+\sqrt y\right)^2, a.s.$ and $s_{\min}\left(\mathbf
S_n\right)\to\left(1-\sqrt y\right)^2,a.s.$ as $n\to\infty$, where $y=\lim
p/n$,
  $s_1\left(\mathbf S_n\right)\le\cdots\le s_{p}\left(\mathbf S_n\right)$ are
the eigenvalues of $\mathbf{S}_n$, $s_{\min}\left(\mathbf
S_n\right)=s_{p-n+1}\left(\mathbf S_n\right)$ when $p>n$ and
$s_{\min}\left(\mathbf S_n\right)=s_1\left(\mathbf S_n\right)$ when $p\le n$.
We also prove that the set of conditions are necessary for
$s_{\max}\left(\mathbf S_n\right)\to\left(1+\sqrt y\right)^2, a.s.$ when the
entries of $\mathbf {X}_n$ are i. i. d.
