Definition:Hadamard Product

Definition
Let $\left({R, +_R, \times_R}\right)$ be a ring.

Let $\mathbf A = \left[{a}\right]_{m n}$ be an $m \times n$ matrix over $R$.

Let $\mathbf B = \left[{b}\right]_{m n}$ be an $m \times n$ matrix over $R$.

Then the Hadamard product of $\mathbf A$ and $\mathbf B$ is written $\mathbf A \circ \mathbf B$ and is defined as follows:


 * $\mathbf A \circ \mathbf B := \mathbf C = \left[{c}\right]_{m n}$

where


 * $\forall i \in \left[{1 \,.\,.\, m}\right], j \in \left[{1 \,.\,.\, n}\right]: c_{i j} = a_{i j} \times_R b_{i j}$

Also known as
Also called the entrywise product or the Schur product.