Notation in linear algebra, what are $N(T)$ and $R(T)$

Question

Working through some stuff I found on the web, I came across a notation that I haven't seen in my textbooks.

In this problem, $ T: P_4(\mathbb R)\rightarrow \mathbb R^4 $ is a linear transformation, and there's a formula given to define it. No problem there.

Then some questions follow, including:

1. Write down a basis for $N(T)$.
2. Write down a basis for $R(T)$.

My question is: What is meant by $N(T)$ and $R(T)$?

Answer 1

1. $N(T)$ is the null-space of $T$, i.e., $N(T)=\{v:T(v)=0\}$
2. $R(T)$ is the range of $T$, i.e., $R(T)=\{T(u): u\in P_4(\mathbb R)\}$