Definition:Scalar Multiplication/Vector Quantity

Definition

Let $\mathbf a$ be a vector quantity.

Let $m$ be a scalar quantity.

The operation of scalar multiplication by $m$ of $\mathbf a$ is denoted $m \mathbf a$ and defined such that:

the magnitude of $m \mathbf a$ is equal to $m$ times the magnitude of $\mathbf a$:

$\size {m \mathbf a} = m \size {\mathbf a}$

the direction of $m \mathbf a$ is the same as the direction of $\mathbf a$.

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
• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 26$. Vector Spaces and Modules
• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 22$: Fundamental Definitions: $2.$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): vector
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): vector