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	2013-03-22 14:03:32
Last modified on	2013-03-22 14:03:32
Owner	drini (3)
Last modified by	drini (3)
Numerical id	6
Author	drini (3)
Entry type	Definition
Classification	msc 15-00
Synonym	trivial vector space
Related topic	ZeroRing
Related topic	ZeroMap