Definition:Scalar Multiplication/Module
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Definition
Let $\struct {G, +_G, \circ}_R$ be an module (either a left module or a right module or both), where:
- $\struct {R, +_R, \times_R}$ is a ring
- $\struct {G, +_G}$ is an abelian group.
The operation $\circ: R \times G \to G$ is called scalar multiplication.
Also known as
Some sources refer to scalar multiplication as exterior multiplication.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Module