zero vector space

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

0.0.1 Properties

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

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

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