zero map
Definition
Suppose X is a set, and Y is a vector space with zero vector 0.
If Z is a map Z:X→Y, such that Z(x)=0 for all x in X,
then Z is a zero map.
0.0.1 Examples
-
1.
On the set of non-invertible n×n matrices, the determinant
is a zero map.
-
2.
If X is the zero vector space, any linear map T:X→Y is a zero map. In fact, T(0)=T(0⋅0)=0T(0)=0.
-
3.
If X=Y and its field is ℝ or ℂ, 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 |