Definition:Matrix Scalar Product/Scalar

This page is about scalar in the context of matrix theory. For other uses, see scalar.

Definition

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.