# Homework Help: Definition of a Restriction in Linear Algebra

1. Nov 27, 2011

### JonoPUH

1. The problem statement, all variables and given/known data
Let V be a finite-dimensional vector over ℝ, and let S and T be linear transformations from V to V

Show that n(ST)≤n(S)+n(T)

Given Hints
Consider the restriction of S to W where W=im(T)

Can someone please tell me what the above hint means?

I haven't attempted a solution, but then I'm not asking for a hint for the solution. I just require the definition of a restriction please! I haven't been able to find a definition of one in my lecture notes. They are just mentioned.

Thanks!

2. Nov 27, 2011

### vela

Staff Emeritus
The restriction simply means you're restricting the domain of S to those vectors in V which are elements of W. In other words, you have a new mapping R: W→V where x maps to S(x) for all x∈W.