I'm wondering how to properly represent a matrix concatenation equation. Consider a set of matrix with indices such that $X_1, X_2,\dots X_K$, then I would like to create a concatenated matrix $W$ with some $X_k$ whose indices are in a subset of $1,\dots,K$, for example $W = [X_1,X_3,X_5]$. Here we define a set $S = \{1,3,5\}$, can I represent $W$ as $W = [X_k|k \in S]$?
Thanks
$ \def\o{{\tt1}} \def\bbR#1{{\mathbb R}^{#1}} \def\LR#1{\left(#1\right)} \def\size#1{\operatorname{size}\LR{#1}} \def\m#1{\left[\begin{array}{c}#1\end{array}\right]} $Let $$\eqalign{ m,n &= \size{X_k} ,\quad m,Kn = \size{W} \\ \quad K,\o &= \size{e_k} ,\quad\;\; Kn,n = \size{E_k} ,\quad n,n = \size{I_n} \\ }$$ where $E_k=(e_k\otimes I_n)$ are block matrix analogs of the Euclidean basis vectors: $\;e_k\in\bbR{K}$
These matrices allow a concatenated matrix to be written as a sum $$W = \sum_{k=\o}^K X_kE_k^T \;=\; \m{X_1&X_2&\cdots&X_K}$$ and for the extraction of a constituent matrix from the concatenation $$X_k = WE_k$$
Your example submatrix can be written in several ways $$\eqalign{ W_S &=\m{X_1&X_3&X_5} \\ &= W\m{E_1&E_3&E_5} \\ &= W\Big(\m{e_1&e_3&e_5}\otimes I_n\Big) \\ }$$
NB: The symbol $\otimes$ is the Kronecker product and $I_n$ is the identity matrix.
Although they appear quite often in Linear Algebra, there's no standard name for matrices like $\m{e_1&e_3&e_5}\:$ although a combination of the adjectives semi-orthogonal and logical seems to cover them.