Definition of spanning/generating set for a space or subspace

Created almost 9 years ago, updated about 8 hours ago

A set $S$ spans or generates $V$ when every vector of $V$ is a finite linear combination of members of $S$, i.e. $\operatorname{span}S=V$. Spanning permits redundancy; a basis additionally requires independence. For example, $e_1,e_2,e_1+e_2$ span $\mathbb R^2$ but are not a basis.

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