Definition of a Restriction in Linear Algebra

[JonoPUH]

Homework Statement

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!

 

[vela]

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.