zero map

Definition Suppose X is a set, and Y is a vector spaceMathworldPlanetmath with zero vector 0. If Z is a map Z:XY, such that Z(x)=0 for all x in X, then Z is a zero map.

0.0.1 Examples

  1. 1.

    On the set of non-invertible n×n matrices, the determinantMathworldPlanetmath is a zero map.

  2. 2.

    If X is the zero vector space, any linear map T:XY is a zero map. In fact, T(0)=T(00)=0T(0)=0.

  3. 3.

    If X=Y and its field is or , then the spectrum of Z is {0}.

Title zero map
Canonical name ZeroMap
Date of creation 2013-03-22 14:03:38
Last modified on 2013-03-22 14:03:38
Owner matte (1858)
Last modified by matte (1858)
Numerical id 6
Author matte (1858)
Entry type Definition
Classification msc 15-00
Related topic ZeroVectorSpace
Related topic ConstantFunction
Related topic IdentityMap
Defines zero operator