Dimension of the subspace T of HomV

brigitte

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L<V is a subspace of vector space V. T is a set of all linear maps from HomV (f : V->V, f is linear map) for which the restriction f|L is a zero map. What is the dimension of T? I tried to find the range of f but I'm obviuosly doing it wrong :-?. Thank you and sorry for my english
 
L<V is a subspace of vector space V. T is a set of all linear maps from HomV (f : V->V, f is linear map) for which the restriction f|L is a zero map. What is the dimension of T? I tried to find the range of f but I'm obviuosly doing it wrong :-?. Thank you and sorry for my english
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Ok. I thought that kernel of f is whole L, because f(a)=0 for all a from L. Now I need to find the image of f, but I'm not sure is it equal to V or not (because f: V->V)? I'm stuck with that :| You don't have to solve it completely, but it would be nice if you give me the idea how to solve it. Thank you!
 
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