The Hadamard product refers to component-wise multiplication of the same dimension. The \(\odot\) symbol is commonly used as the Hadamard product operator.

Here is an example for the Hadamard product for a pair of \(3 \times 3\) matrices.

\[ \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \odot \begin{bmatrix} j & k & l \\ m & n & o \\ p & q & r \end{bmatrix} = \begin{bmatrix} aj & bk & cl \\ dm & ne & fo \\ gp & hq & ir \end{bmatrix} \]