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).Copy