Vector subspaces of zero dimension I was confused about zero dimension vector subspaces. Can you please answer the following questions with details/examples.


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*What is the dimension and basis for vector space that is just composed of the zero vector.

*If the answer to the latter is an empty set, how can I construct a zero vector of say n rows from the empty set?

*Say there are three vector spaces [0]  [0, 0] [0 ,0, 0]. What are the basis for them. Isn't just saying empty set led to ambiguity about the zero vector subspace, it is a basis for?

Here is a proof:
Let us assume that $\mathscr B$ is a basis of $\{0\}$.
Then since $\mathscr B$ is a subset of  $\{0\}$ so $\mathscr B=\{0\}$ or $\mathscr B=\emptyset$. If it has to be non-empty then $\mathscr B=\{0\}$
But $\{0\}$ is not linearly independent how can it be a basis.
