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Definition of a Restriction in Linear Algebra

  1. Nov 27, 2011 #1
    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. jcsd
  3. Nov 27, 2011 #2

    vela

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    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.
     
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