If V is any vector space over F, the zero subspace of V is spanned by the vector 0, but {0} is a linearly dependent set and not a basis. For this reason, we shall agree that the zero subspace has dimension 0. Alternatively we could reach the same conclusion by arguing that the empty set is a basis for the zero subspace. The empty set spans {0}, because the intersection of all subspaces containing the empty set is {0}, and the empty set is linearly independent because it contains no vectors.


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