25 - Types of Linear Maps

Identity Map

Let $V$ be a vector space then
The identity map is $i{d}_V:V\to V$ is defined by

$$i{d}_V(v)=v\text{ for all }v\in V$$

It is also a linear map

Zero Map

Let $V,W$ be vector spaces
The zero map is $0:V\to W$ is defined by

$$0(v)=0_W\text{ for all }v\in V$$

It is also a linear map
Notation may look confusing but the map $0$ is a function