Category:Examples of Matrix Entrywise Addition

This category contains examples of 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.