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.
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© 1970 Springer-Verlag Berlin · Heidelberg
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Stoer, J., Witzgall, C. (1970). Convex Polyhedra. In: Convexity and Optimization in Finite Dimensions I. Die Grundlehren der mathematischen Wissenschaften, vol 163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46216-0_3
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DOI: https://doi.org/10.1007/978-3-642-46216-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-46218-4
Online ISBN: 978-3-642-46216-0
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