pat_connell
Aug22-04, 08:56 AM
Hey guys,
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!
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!