# Definition:Zero Subspace

(Redirected from Definition:Trivial Subspace)

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## Definition

Let $V$ be a vector space with zero vector $\mathbf 0$.

Then the set $(\mathbf 0) := \left\{{\mathbf 0}\right\}$ is called the **zero subspace** of $V$.

This name is appropriate as $(\mathbf 0)$ is in fact a subspace of $V$, as proved in Zero Subspace is Subspace.

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