A very short algebraic proof of the Farkas Lemma

David Bartl ()

Mathematical Methods of Operations Research, 2012, vol. 75, issue 1, 104 pages

Abstract: We present a very short algebraic proof of a generalisation of the Farkas Lemma: we set it in a vector space of finite or infinite dimension over a linearly ordered (possibly skew) field; the non-positivity of a finite homogeneous system of linear inequalities implies the non-positivity of a linear mapping whose image space is another linearly ordered vector space. In conclusion, we briefly discuss other algebraic proofs of the result, its special cases and related results. Copyright Springer-Verlag 2012

Keywords: Farkas Lemma; Systems of linear inequalities; 15A39; 06F20; 12J15 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s00186-011-0377-y

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