Definition:Scalar Multiplication/Vector Space
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Definition
Let $\struct {G, +_G, \circ}_K$ be a vector space, where:
- $\struct {K, +_K, \times_K}$ is a field
- $\struct {G, +_G}$ is an abelian group.
The operation $\circ: K \times G \to G$ is called scalar multiplication.
Also known as
Some sources refer to scalar multiplication as exterior multiplication.
Also see
- Results about scalar multiplication can be found here.
Sources
- 1961: I.M. Gel'fand: Lectures on Linear Algebra (2nd ed.) ... (previous) ... (next): $\S 1$: $n$-Dimensional vector spaces
- 1965: Claude Berge and A. Ghouila-Houri: Programming, Games and Transportation Networks ... (previous) ... (next): $1$. Preliminary ideas; sets, vector spaces: $1.2$. Vector Spaces
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 26$. Vector Spaces and Modules
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): vector space
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.26$: Extensions of the Complex Number System. Algebras, Quaternions, and Lagrange's Four Squares Theorem
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions: Definition $2.1.2$