Matrix Multiplication

Matrix Multiplication

## Formula

If $$a$$ is of order $m\times n$ and $$b$$ is of order $n\times p$, then:

$$AB=C$$

where $$c$$ is of order:

$$m\times p$$

and:

$$c_{ij}=\sum_{k=1}^{n}a_{ik}b_{kj}$$

## Condition

The number of columns of $$a$$ must equal the number of rows of $$b$$.

## Usage

- Used to multiply matrices and represent systems of linear transformations.