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Convex Polyhedra

  • Josef Stoer
  • Christoph Witzgall
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 163)

Abstract

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.

Keywords

Boundary Plane Face Lattice Convex Polyhedron Lineality Space Polyhedral Cone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1970

Authors and Affiliations

  • Josef Stoer
    • 1
  • Christoph Witzgall
    • 2
  1. 1.Universität WürzburgDeutschland
  2. 2.Boeing Scientific Research LaboratoriesSeattleUSA

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