\begin{definition}[Definition:Matrix Scalar Product/Scalar]
Let $\map \MM {m, n}$ be a matrix space of order $m \times n$ on which scalar multiplication is defined.
Let $\mathbf A = \sqbrk a_{m n} \in \map \MM {m, n}$.
Let $\lambda$ be an element of the underlying structure such that:
:$\mathbf C = \lambda \mathbf A$
where the notation denotes scalar multiplication.
The element $\lambda$ of the underlying structure of $\map \MM {m, n}$ is known as a '''scalar'''.
Category:Definitions/Matrix Products
\end{definition}