This quantity includes a choice of shrewdpermanent mathematical functions of linear algebra, more often than not in combinatorics, geometry, and algorithms. each one bankruptcy covers a unmarried major end result with motivation and whole evidence in at such a lot ten pages and will be learn independently of all different chapters (with minor exceptions), assuming just a modest historical past in linear algebra. the themes contain a couple of famous mathematical gemstones, corresponding to Hamming codes, the matrix-tree theorem, the Lovász sure at the Shannon capability, and a counterexample to Borsuk's conjecture, in addition to different, maybe much less renowned yet equally attractive effects, e.g., quick associativity checking out, a lemma of Steinitz on ordering vectors, a monotonicity end result for integer walls, or a certain for set pairs through external items. the better ends up in the 1st a part of the booklet supply abundant fabric to brighten up an undergraduate process linear algebra. The extra complex components can be utilized for a graduate process linear-algebraic equipment or for seminar displays.
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