# Definition:Hadamard Product

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## Definition

Let $\mathbf A = \sqbrk a_{m n}$ and $\mathbf B = \sqbrk b_{m n}$ be $m \times n$ matrices over a ring $\struct {R, +, \times}$.

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:

- $\forall i \in \closedint 1 m, j \in \closedint 1 n: c_{i j} = a_{i j} \times b_{i j}$

### Defined Operation

It needs to be noted that the operation of **Hadamard product** is defined only when both matrices have the same number of rows and the same number of columns.

## Also known as

The **Hadamard product** is also known as:

- the
**(matrix) entrywise product** - the
**Schur product**, for Issai Schur.

## Also see

- Results about
**Hadamard product**can be found**here**.

## Source of Name

This entry was named for Jacques Salomon Hadamard.

## Sources

- 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Hadamard product**