This chapter starts to deviate from the canonical stuff of undergraduate linear algebra; we briefly discuss basic properties of an arrangement of several hyperplanes in affine space—this is already a surprisingly rich structure with some beautiful and hard mathematics.
Our exposition follows the classical treatment of the subject by Bourbaki [Bou], with slight changes in terminology. All the results mentioned in this section are intuitively self-evident, at least after drawing a few simple pictures. We omit some of the proofs, which can be found in [Bou, Chap. V, §1].
KeywordsRich Structure Hyperplane Arrangement Geometric Intuition Open Convex Subset Nontrivial Intersection
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