Definition:Scalar Multiplication by Negative Scalar

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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 $\mathbf a$.