##### Definition3.5.7

A basis for a subspace $$S$$ of $$\real^p$$ is a set of vectors in $$S$$ that are linearly independent and span $$S\text{.}$$ It can be seen that any two bases have the same number of vectors. Therefore, we say that the dimension of the subspace $$S\text{,}$$ denoted $$\dim S\text{,}$$ is the number of vectors in any basis.

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