Span of a Set of Linear Transformations

  • #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).
 

Answers and Replies

  • #2
Stephen Tashi
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Are V,W finite dimensional vector spaces?
 
  • #3
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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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