zero vector space

Definition A zero vector space is a vector spaceMathworldPlanetmath 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 dimensionPlanetmathPlanetmath 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(00)=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