The first chapter dealt with the logical structure of linear systems. This chapter directs the attention to the geometrical properties of their solution sets. Nevertheless, we shall reestablish some of the results of the first chapter, such as the lemma of Farkas (1.4.8), and the transposition theorem of Gordan (1.6.3). Both are equivalent formulations of what is sometimes called the “key fact” of the theory of linear inequalities. To this class of theorems also belong the theorem of Weyl (2.8.8) and the theorem of Kuhn-Fourier (1.1.9), on which the first chapter was based.
KeywordsBoundary Plane Face Lattice Convex Polyhedron Lineality Space Polyhedral Cone
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