The set containing only 0 is a vector space.

Theorem: The set ({\mathbf{0}}) containing only the zero vector is a vector space over any field (\mathbb{F}).

Verification: With the only possible operations ( \mathbf{0} + \mathbf{0} = \mathbf{0}) and (c \cdot \mathbf{0} = \mathbf{0}) for all (c \in \mathbb{F}), all ten vector space axioms are trivially satisfied.

This is called the trivial or zero vector space. It has dimension 0 and is a subspace of every vector space.

It is the unique vector space of dimension 0 (up to isomorphism).