Asymptotic Distribution of eigenvalues and eigenvectors Let $\mathbf{A}\in\mathbb{R}^{n\times n}$ be a random matrix. Now consider the following two cases:

*

*Suppose $n$ is fixed and is a small number less than 100. If I take sufficiently large samples, N, (N >10000) of $\mathbf{A}$ and find the resultant distribution of the eigenvalues/vectors, can I call it asymptotic or limiting distribution?


*n is not fixed. If the distribution of eigenvalue/vectors is based on the limit as $n\rightarrow\infty$ and $N\rightarrow\infty$, can I call it asymptotic distribution?
So, which of the two can be called asymptotic distribution of eigenvalues/vectors?

Both of those are
"asymptotic distribution of eigenvalues/vectors".
In one, 
you are letting the number of samples grow;
in the other,
you are letting the
size of the samples grow.
Different questions
which may have 
different distributions.
