# Span of a Set of Linear Transformations

1. Nov 11, 2013

### jsgoodfella

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. Nov 17, 2013

### Stephen Tashi

Are V,W finite dimensional vector spaces?

3. Nov 17, 2013

### PSarkar

The idea is to consider some arbitrary linear transformation $T \in \mathcal{L}(V, W)$ 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.