Definition:Spanning Set

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Spanning Set may refer to:

Spanning Set of Module

$S$ is a generator of $M$ if and only if $M$ is the submodule generated by $S$.


Spanning Set of Vector Space

Let $K$ be a division ring.

Let $\mathbf V$ be a vector space over $K$.

Let $S \subseteq \mathbf V$ be a subset of $\mathbf V$.


$S$ is a generator of $\mathbf V$ if and only if every element of $\mathbf V$ is a linear combination of elements of $S$.