Definition:Matrix Product (Conventional)/Pre-Multiplication

Definition
Let $\struct {R, +, \circ}$ be a ring.

Let $\mathbf A = \sqbrk a_{m n}$ be an $m \times n$ matrix over $R$.

Let $\mathbf B = \sqbrk b_{n p}$ be an $n \times p$ matrix over $R$.

Let $\mathbf A \mathbf B$ be the product of $\mathbf A$ with $\mathbf B$.

Then $\mathbf B$ is pre-multiplied by $\mathbf A$.

Also known as
Some sources render it without the hyphen: premultiplication.

Also see

 * Definition:Post-Multiplication