Definition:Scalar Multiplication by Negative Scalar

Definition

Let $\mathbf a$ be a vector quantity.

Let $-m$ be a negative scalar quantity.

The operation of scalar multiplication by $-m$ of $\mathbf a$ is defined as:

$-m \mathbf a := \paren {-m} \mathbf a = m \paren {-\mathbf a}$

that is, the negative of the scalar product of $m$ with $\mathbf a$.

Sources

• 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Addition and Subtraction of Vectors: $5$. Multiplication by a number