# zero vector space

Definition A zero vector space is a vector space that contains only one element, a zero vector.

## 0.0.1 Properties

1. 1.

Every vector space has a zero vector space as a vector subspace.

2. 2.

A vector space $X$ is a zero vector space if and only if the dimension of $X$ is zero.

3. 3.

Any linear map defined on a zero vector space is the zero map. If $T$ is linear on $\{0\}$, then $T(0)=T(0\cdot 0)=0T(0)=0$.

Title zero vector space ZeroVectorSpace 2013-03-22 14:03:32 2013-03-22 14:03:32 drini (3) drini (3) 6 drini (3) Definition msc 15-00 trivial vector space ZeroRing ZeroMap