The vector space * Linear combinations ** Linear combinations: JunkCo ** Lights Out * Span *** Span: Attacking the authentication scheme ** Generators ** Standard generators * Geometry of sets of vectors: span of vectors over R * Geometry of sets of vectors: Two representations ** Two representations: What's common? * Abstract vector spaces * Geometric objects that exclude the origin ** Affine space *** Affine space and affine combination *** Geometric objects not containing the origin: equations *** The solution set of a linear system is either empty or an affine space **** Number of solutions to a linear system * Geometry of sets of vectors: convex hull * %%% Local Variables: %%% mode: org %%% eval: (auto-fill-mode t) %%% eval: (flyspell-mode t) %%% End: