zero map
Definition Suppose $X$ is a set, and $Y$ is a vector space^{} with zero vector $0$. If $Z$ is a map $Z:X\to Y$, 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 noninvertible $n\times n$ matrices, the determinant^{} is a zero map.

2.
If $X$ is the zero vector space, any linear map $T:X\to Y$ is a zero map. In fact, $T(0)=T(0\cdot 0)=0T(0)=0$.

3.
If $X=Y$ and its field is $\mathbb{R}$ or $\u2102$, then the spectrum of $Z$ is $\{0\}$.
Title  zero map 

Canonical name  ZeroMap 
Date of creation  20130322 14:03:38 
Last modified on  20130322 14:03:38 
Owner  matte (1858) 
Last modified by  matte (1858) 
Numerical id  6 
Author  matte (1858) 
Entry type  Definition 
Classification  msc 1500 
Related topic  ZeroVectorSpace 
Related topic  ConstantFunction 
Related topic  IdentityMap 
Defines  zero operator 