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.
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 $X$ is zero.

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 

Canonical name  ZeroVectorSpace 
Date of creation  20130322 14:03:32 
Last modified on  20130322 14:03:32 
Owner  drini (3) 
Last modified by  drini (3) 
Numerical id  6 
Author  drini (3) 
Entry type  Definition 
Classification  msc 1500 
Synonym  trivial vector space 
Related topic  ZeroRing 
Related topic  ZeroMap 