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Span of a Set of Linear Transformations

  1. Nov 11, 2013 #1
    How do you show that a set of linear transformations from one vector space to another spans L(V,W)?


    This isn't a homework question, or even a question that's in the text I'm reading (Friedberg).
     
  2. jcsd
  3. Nov 17, 2013 #2

    Stephen Tashi

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    Are V,W finite dimensional vector spaces?
     
  4. Nov 17, 2013 #3
    The idea is to consider some arbitrary linear transformation [itex]T \in \mathcal{L}(V, W)[/itex] and show that it can be written as a linear combination of the linear transformations in the set. Its hard to give any more details without seeing the actual question. Is the set a basis? Is it the standard basis? etc. If you can give the page number and question number, I can help since I have the book.
     
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