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.
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Bartl, D. A very short algebraic proof of the Farkas Lemma. Math Meth Oper Res 75, 101–104 (2012). https://doi.org/10.1007/s00186-011-0377-y
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DOI: https://doi.org/10.1007/s00186-011-0377-y