Notation for stacking vectors and defining matrices whose columns are vectors

Question

I have perhaps a silly question. I have a set of vectors $\xi_\ell$, with $\ell\in J_k\subset \{1,\ldots,k\}$. Now I want to create a long vector $\xi$ where these individual vectors are stacked on top of each other, and a matrix $\Xi$ of which the columns are these individual vectors.

I am stuck with the proper notation. I cannot use the traditional way where, for example, $\ell\in\{1,\ldots,k\}$, I can define $\xi:=[\xi_1^\top,\ldots,\xi_k^\top]^\top$, since in my case the $\ell$ may not be contiguous or start at $1$. Similar problem for defining the matrix $\Xi$.

Does anyone have a suggestion or is anyone aware of the proper way defining this vector and matrix?

Thanks a lot!

Answer 1

I would not mind \begin{align} \xi &= (\xi_{l_1}^\top, \dotsc, \xi_{l_n}^\top)^\top \quad (l_i \in J_k, i \in J_n, n \le k) \\ \Xi &= (\xi_{l_1}, \dotsc, \xi_{l_n}) \end{align}