Definition:Generator of Vector Space/Also known as
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Generator of Vector Space: Also known as
A generator of a vector space is also known as a spanning set.
Some sources refer to a generator for rather than generator of. The two terms mean the same.
It can also be said that $S$ generates $\mathbf V$ (over $K$).
Other terms for $S$ are:
- A generating set of $\mathbf V$ (over $K$)
- A generating system of $\mathbf V$ (over $K$)
Some sources refer to such an $S$ as a set of generators of $\mathbf V$ over $K$ but this terminology is misleading, as it can be interpreted to mean that each of the elements of $S$ is itself a generator of $\mathbf V$ independently of the other elements.