Definition:Spanning Set

Definition

Let $G$ be a vector space over a field $F$.

Let $S \subseteq G$.

Then $S$ is a spanning set (for $G$, or of $G$) iff every vector of $G$ can be expressed as a linear combination of elements of $S$.

That is, iff $S$ is a generator for $G$.

If this is the case, then $S$ spans $G$.

Sources

• John F. Humphreys: A Course in Group Theory (1996): $\text{A}.2$: Definition $\text{A}.5$