Definition:Scalar/Vector Space
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This page is about scalar in the context of linear algebra. For other uses, see scalar.
Definition
Let $\struct {G, +_G, \circ}_K$ be a vector space, where:
- $\struct {G, +_G}$ is an abelian group
- $\struct {K, +_K, \times_K}$ is the scalar field of $\struct {G, +_G, \circ}_K$.
The elements of the scalar field $\struct {K, +_K, \times_K}$ are called scalars.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 26$. Vector Spaces and Modules
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $7$: Vector Spaces: $\S 32$. Definition of a Vector Space
- 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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): scalar: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): scalar: 1.