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I have a theoretical question on subspaces. Consider the space R

^{n}. The zero vector is indeed a subspace of R

^{n}. However, if I am not mistaken, the zero vector has no orthonormal basis, even though it is a subspace. I thought all subspaces have an orthonormal basis (or is it all subspaces of n dimensions?). Can anyone shed any light on where I am going wrong here?

Thanks