# Category:Matrix Entrywise Addition

This category contains results about **Matrix Entrywise Addition**.

Let $\mathbf A$ and $\mathbf B$ be matrices of numbers.

Let the orders of $\mathbf A$ and $\mathbf B$ both be $m \times n$.

Then the **matrix entrywise sum of $\mathbf A$ and $\mathbf B$** is written $\mathbf A + \mathbf B$, and is defined as follows:

Let $\mathbf A + \mathbf B = \mathbf C = \sqbrk c_{m n}$.

Then:

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

Thus $\mathbf C = \sqbrk c_{m n}$ is the $m \times n$ matrix whose entries are made by performing the adding corresponding entries of $\mathbf A$ and $\mathbf B$.

That is, the **matrix entrywise sum of $\mathbf A$ and $\mathbf B$** is the **Hadamard product** of $\mathbf A$ and $\mathbf B$ with respect to addition of numbers.

This operation is called **matrix entrywise addition**.

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Matrix Entrywise Addition"

The following 11 pages are in this category, out of 11 total.

### M

- Matrix Entrywise Addition forms Abelian Group
- Matrix Entrywise Addition is Associative
- Matrix Entrywise Addition is Commutative
- Matrix Entrywise Addition over Ring is Associative
- Matrix Entrywise Addition over Ring is Closed
- Matrix Entrywise Addition over Ring is Commutative
- Matrix Multiplication Distributes over Matrix Addition