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I have a little problem here:

given two subspaces U and W both of dimension two of an N dimensional space show in general that if N = 3 the intersection of U and W forms a curve; if N = 4 a finite number of points; and N > 4 they do not in general intersect at all.

I can kind of visualize the answer for the first two cases based on analagous cases lines viewed in R2 and R3, but I am not really satisfied with the answers.

I would like a really rigorous maths proof.

please help!

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# Intersecting subspaces in N dimensions

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