Definition:Multiplication/Multiplier

Definition
Let $a \times b$ denote the operation of multiplication on two objects.

The objects $a$ is known as the multiplier of $b$.

That is, it is the object which is to multiply the multiplicand.

Note that the nature of $a$ and $b$ has deliberately been left unspecified.

They could be, for example, numbers, matrices or more complex expressions constructed from such elements.

Also known as
In algebraic systems where multiplication is commutative, it is commonplace to treat both the multiplier and multiplicand as the same sort of object, and refer to them both as factors.