I'm trying to find the proper operator for a column wise multiplication. Consider $v=[v_1, v_2, ..., v_n]^T$ and $$A=\begin{bmatrix} a_{1,1} & a_{1,2} & a_{1,3} \\a_{2,1} & a_{2,2} & a_{2,3} \\ a_{3,1} & a_{3,2} & a_{3,3}\end{bmatrix},$$
so that such operation would be:
$$ v \diamond A = \begin{bmatrix} a_{1,1} v_1 & a_{1,2} v_1 & a_{1,3} v_1 \\a_{2,1} v_2 & a_{2,2} v_2 & a_{2,3} v_2 \\ a_{3,1} v_3 & a_{3,2} v_3 & a_{3,3} v_3 \end{bmatrix}$$
Each column of $A$ is multiplied by the vector $v$. If there is no such operator, how can I define it?