Any body knows the name of the product $A\circ B$, It is not Hadamard tensor product

Question

I have seen this operation in a vectorization operation of $D=AX^{T}B$ i.e. $vec(D)=\left( A\circ B\right) vec(X),$ \begin{equation*} A\circ B= \begin{pmatrix} A_{1}B_{1}^{T} & A_{2}B_{1}^{T} & \cdots & A_{n}B_{1}^{T} \\ A_{1}B_{2}^{T} & A_{2}B_{2}^{T} & \cdots & A_{n}B_{2}^{T} \\ \vdots & \vdots & \ddots & \vdots \\ A_{1}B_{n}^{T} & A_{2}B_{n}^{T} & \cdots & A_{n}B_{n}^{T} \end{pmatrix}, \end{equation*} where $A_{j}$, $B_{j}$, $j=1,2,\cdots ,N,$ denoting the column vector of $A$ and $B,$ respectively.