Proper notation for Random Matrix and observation My question is simple, but I could not find any references for this particular case.
When we have a random vector, we usually use $\boldsymbol{X}$ to denote the random vector and $\boldsymbol{x}$ to denote an observation of this random vector.
Now, when we use matrices, the usual notation for a matrix is a non-bold upper-case letter (e.g. $X$). In this case, what is the proper (or most usual) notation in order to distinguish the random matrix and the matrix of observations?

In the case of an IID sample ${\bf X}_1, \ldots, {\bf X}_n$, where ${\bf X}_i$ is a $p\times 1$ random vector, to denote a random matrix of all samples I prefer to use the Blackboard bold typeface
$$
\mathbb{X} = [{\bf X}_1|\cdots |{\bf X}_n].
$$
Yes, this matrix has dimension $p\times n$ and not $n\times p$, but it has its advantages, at least in multivariate analysis. It is used also by others, e.g. Koch (2014) Analysis of Multivariate and High-Dimensional Data, ISBN: 9780521887939.
In the case of an observed sample ${\bf x}_1, \ldots, {\bf x}_n$, I use
$$
\mathbb{x} = [{\bf x}_1|\cdots |{\bf x}_n].
$$
If you use LaTeX, to produce lower-case letters in Blackboard bold typeface, e.g. $\mathbb{x}$, you'll have to use the bbm package.
