Hadamard product

Remarks

Example: for $A = \begin{pmatrix} 1 & 0 & 2 \end{pmatrix}$ and $B = \begin{pmatrix} 3 & 5 & -1 \end{pmatrix}$, the entries of $A \circ B$ are $1 \cdot 3$, $0 \cdot 5$ and $2 \cdot (-1)$, so $A \circ B = \begin{pmatrix} 3 & 0 & -2 \end{pmatrix}$. Non-example: a $2 \times 2$ matrix and a $2 \times 3$ matrix have no Hadamard product, because the two matrices must have the same size. The Hadamard product is commutative, associative and distributive over addition. Its identity element is the $m \times n$ matrix $J$ with all entries $1$, not the identity matrix. Other notations are $A \odot B$ and $A * B$.