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) is a linearly independent subset of that spans . This means that a subset of is a basis if it satisfies the two following conditions:
* linear independence: for every finite subset of , if for some in , then ; and
* the spanning property: for every vector in , one can choose in and in such that $\backslash mathbf\; v\; =\; a\_1\; \backslash mathbf\; v\_1\; +\; \backslash cdots\; +\; a\_n\; \backslash mathbf\; v\_n$. In other words,

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