Overview
The hadamard product of two matrices of the same dimensions, is the element by element \ multiplication.
{%
\begin{bmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23}\\
a_{31} & a_{32} & a_{33} \\
\end{bmatrix}
\times
\begin{bmatrix}
b_{11} & b_{12} & b_{13} \\
b_{21} & b_{22} & b_{23}\\
b_{31} & b_{32} & b_{33} \\
\end{bmatrix}
=
\begin{bmatrix}
a_{11}b_{11} & a_{12}b_{12} & a_{13}b_{13} \\
a_{21}b_{21} & a_{22}b_{22} & a_{23}b_{23}\\
a_{31}b_{31} & a_{32}b_{32} & a_{33}b_{33} \\
\end{bmatrix}
%}