Kronecker product is a mathmatical tools to find all possible combination of something. It can be used for many combinational problem like Traveling-salesman problem.
Now, kronecker product $\otimes$ defines like follow.
For $A$ $=$ $\begin{pmatrix}A_{1,1} & A_{1,2} & \cdots & A_{1,n}\\ A_{2,1} & A_{2,2} & \cdots & A_{2,n}\\ \vdots & \vdots & \ddots & \vdots\\ A_{m,1} & A_{m,2} & \cdots & A_{m,n}\\ \end{pmatrix}$, $B$ $=$ $\begin{pmatrix}B_{1,1} & B_{1,2} & \cdots & B_{1,p}\\ B_{2,1} & B_{2,2} & \cdots & B_{2,p}\\ \vdots & \vdots & \ddots & \vdots\\ B_{q,1} & B_{q,2} & \cdots & B_{q,p}\\ \end{pmatrix}$,
$A \otimes B$ $=$ $\begin{pmatrix}A_{1,1}B & A_{1,2}B & \cdots & A_{1,n}B\\ A_{2,1}B & A_{2,2}B & \cdots & A_{2,n}B\\ \vdots & \vdots & \ddots & \vdots\\ A_{m,1}B & A_{m,2}B & \cdots & A_{m,n}B\\ \end{pmatrix}$ $=$ $\begin{pmatrix}A_{1,1}B_{1,1} & A_{1,1}B_{1,2} & \cdots & A_{1,1}B_{1,p} & A_{1,2}B_{1,1} & A_{1,2}B_{1,2} & \cdots & A_{1,2}B_{1,p} & A_{1,3}B_{1,1} & \cdots & A_{1,n}B_{1,p}\\ A_{1,1}B_{2,1} & A_{1,1}B_{2,2} & \cdots & A_{1,1}B_{2,p} & A_{1,2}B_{2,1} & A_{1,2}B_{2,2} & \cdots & A_{1,2}B_{2,p} & A_{1,3}B_{2,1} & \cdots & A_{1,n}B_{2,p}\\ \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ A_{1,1}B_{q,1} & A_{1,1}B_{q,2} & \cdots & A_{1,1}B_{q,p} & A_{1,2}B_{q,1} & A_{1,2}B_{q,2} & \cdots & A_{1,2}B_{q,p} & A_{1,3}B_{q,1} & \cdots & A_{1,n}B_{q,p}\\ A_{2,1}B_{1,1} & A_{2,1}B_{1,2} & \cdots & A_{2,1}B_{1,p} & A_{2,2}B_{1,1} & A_{2,2}B_{1,2} & \cdots & A_{2,2}B_{1,p} & A_{2,3}B_{1,1} & \cdots & A_{2,n}B_{1,p}\\ A_{2,1}B_{2,1} & A_{2,1}B_{2,2} & \cdots & A_{2,1}B_{2,p} & A_{2,2}B_{2,1} & A_{2,2}B_{2,2} & \cdots & A_{2,2}B_{2,p} & A_{2,3}B_{2,1} & \cdots & A_{2,n}B_{2,p}\\ \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ A_{2,1}B_{q,1} & A_{2,1}B_{q,2} & \cdots & A_{2,1}B_{q,p} & A_{2,2}B_{q,1} & A_{2,2}B_{q,2} & \cdots & A_{2,2}B_{q,p} & A_{2,3}B_{q,1} & \cdots & A_{2,n}B_{q,p}\\ \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ A_{m,1}B_{q,1} & A_{m,1}B_{q,2} & \cdots & A_{m,1}B_{q,p} & A_{m,2}B_{q,1} & A_{m,2}B_{q,2} & \cdots & A_{m,2}B_{q,p} & A_{m,3}B_{q,1} & \cdots & A_{m,n}B_{q,p}\\ \end{pmatrix}$.
Notice that this can be used for something recursive because it copies $B$s to submatrices.