Definition:Linear Combination/Subset
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Definition
Let $M = \struct {G, +_G, \circ}_R$ be an $R$-module.
Let $\O \subset S \subseteq G$.
Let $b \in M$ be a linear combination of some sequence $\sequence {a_n}$ of elements of $S$.
Then $b$ is a linear combination of $S$.
Also see
- Definition:Linear Combination
- Definition:Linear Combination of Sequence
- Definition:Linear Combination of Empty Set
Sources
- 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 4$. Vector Spaces
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 27$. Subspaces and Bases