A Simple Proof for a Characterization of Sign-Central Matrices Using Linear Duality

Rico Zenklusen
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Rico Zenklusen: ETH Zurich, Institute for Operations Research

Chapter 88 in Operations Research Proceedings 2008, 2009, pp 545-548 from Springer

Abstract: Summary We consider a problem described in 1992 by Davidov and Davidova, where for a given matrix A ⊆m×n we want to know whether every matrix B ⊆ Rm×n with the same sign pattern as A has a nonnegative, nonzero element in its null-space. Such a matrix A is called sign-central. Davidov and Davidova gave a characterization of sign-central matrices that was proven by a rather long argument. In this paper we present a simple proof showing that the aforementioned characterization of sign-central matrices can be seen as a consequence of the weak duality theorem of linear programming

Date: 2009
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DOI: 10.1007/978-3-642-00142-0_88

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