Let $f: V \rightarrow V$ be a bijective map of a vector space to itself that preserves one-dimensional affine subspaces. Is $f$ already the composition of some invertible matrix and a translation? My intuition says yes, but writing down a matrix didn't work. Thanks!
Map preserving one-dimensional affine subspaces is affine
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linear-algebra
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0I read Jeffers' article, and while it was very interesting, he works over the affine plane. I am not sure if this holds over arbitrary fields, or at least his proof doesn't seem to be applicable to the general case. Does anybody have any more information? I may assume that the ground field is finite, if this helps. – 2012-06-13