What notation to use for stacking a series of matrices?

Question

I have a series of matrices that I need to stack on top of each other, and use the resulting tall matrix - in fact, several such matrices, each stacking different components - in a formula. I would like a compact symbol for it, something along the lines of $\sum_i A_i$ for sum or $\prod_i A_i$ for product. I know the regular way is $\left[\substack{A_1\\ \vdots \\ A_n}\right]$, but it's way too bulky for my purposes.

Answer 1

There is no single widely used notation for this. One common notation is $\mathrm{col}(A_1,\dots,A_n)$. Another common solution is to use "Matlab notation" and write $[A_1; \cdots; A_n]$. Another solution you might consider (though I don't know how common it is) is to write $[A_i]_{i=1}^n$. More commonly, the latter solution is used for block matrices, as in $$ [A_{ij}]_{i=1,j=1}^{m,\quad n} = \pmatrix{A_{11} & \cdots & A_{1n}\\ \vdots & \ddots & \vdots\\ A_{m1} & \cdots & A_{mn}}. $$