Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $R(T)$?

share|improve this question
    
+1. Well posed question! –  user21436 Feb 5 '12 at 8:49
    
Sometimes the null space of $T$ we call the kernel of $T$ too. But if I'm not wrong the null space is a term used mainly in linear algebra whereas the term "kernel" can be used in more settings such as the kernel of a group/ring homomorphism or the kernel of a linear transformation. –  user38268 Feb 5 '12 at 9:49

1 Answer 1

up vote 4 down vote accepted
  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., $R(T)=\{T(u): u\in P_4(\mathbb R)\}$
share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.