Im trying to understand an operation in a paper of Statitstics. In simplified terms, the operation is :
$$A = \bigotimes_{j=1}^J \begin{bmatrix} a_j \\ b_j \end{bmatrix}$$
where $\begin{bmatrix} a_j \\ b_j \end{bmatrix}$ denotes a matrix with $a_j,b_j \in \mathbb{R}$ and $J \in \mathbb{N}$.
What is the meaning of $\bigotimes_{j=1}^J$ operator (and, for curiosity, how it is called)?
For example, if $J=3$, what is resulting matrix $A$?