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Let F be a field and X a set. The functions from X to F form an F… - Problem-A-Day

rdoreApr. 9th, 2008 04:00 pm

Let F be a field and X a set. The functions from X to F form an F vector space. Let A be a set of linearly independent functions from X to F. Prove that there is Y a subset of X, with |Y|=|A| so that

{f restricted to Y : f in A}

is linearly independent (in the space of functions from Y to F).

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