A set of vectors containing fewer elements than the dimension of the space cannot span

Created almost 9 years ago, updated about 8 hours ago

In a finite-dimensional space of dimension $n$, fewer than $n$ vectors cannot span. The dimension of the span of $k$ vectors is at most $k$, as a basis can be extracted from the list. Thus at least $n$ generators are necessary, though having $n$ or more is not sufficient.

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