Category:Definitions/Generators of Vector Spaces

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This category contains definitions related to Generators of Vector Spaces.
Related results can be found in Category:Generators of Vector Spaces.

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 $S$.