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- Thread starter JamesTheBond
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radou

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What exactly do you mean? A basis for V is a span for W.

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matt grime

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Anyway, the original question is not very clear. There is no such thing as *the* basis of a vector space. And I don't know what it means for one basis to span a basis of subset.

If you mean: given W<V, and a basis set B for V, does B have a subset that is a basis for W, then the answer is no.

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I believe this is the basis extension theorem... not sure.

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radou

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For W < V, B_W (some basis of W) is linearly independent and spans W, therefore, there exists some B_V (basis of V) s.t. B_W < B_V.

I believe this is the basis extension theorem... not sure.

I'm not sure what B_W < B_V is supposed to mean, but if you meant that every linearly independent set in a vector space V (and hence a basis of a subspace W, too, since it's a linearly independent set) can be 'extended to the basis' of V, then the answer is yes.

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Sorry, I meant to say: for some [tex] B_W \subset B_V [/tex] for some basis of V.

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HallsofIvy

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Let {v

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mathwonk

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HallsofIvy

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Interesting but simple question. Since that is a one dimensional subspace and (1,0)+ (0,1)= (1,1) is in the space, {(1,0)+ (0,1)} is a basis for the subspace.

However, in case this confuses any one, the original question asked here was "if you had a basis for that subspace, how would you get a basis for R

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