\begin{definition}[Definition:Hadamard Product]
Let $\struct {S, \cdot}$ be an algebraic structure.
Let $\mathbf A = \sqbrk a_{m n}$ be an $m \times n$ matrix over $S$.
Let $\mathbf B = \sqbrk b_{m n}$ be an $m \times n$ matrix over $S$.
The '''Hadamard product of $\mathbf A$ and $\mathbf B$''' is written $\mathbf A \circ \mathbf B$ and is defined as follows:
:$\mathbf A \circ \mathbf B := \mathbf C = \sqbrk c_{m n}$
where:
:$\forall i \in \closedint 1 m, j \in \closedint 1 n: c_{i j} = a_{i j} \cdot_R b_{i j}$
\end{definition}