On pairs of complementary GJ pivoting transforming skew-symmetric matrices

Abstract

This article describes certain ratios that attend pairs of complementary Gauss-Jordan pivotings transforming skew-symmetric matrices. Our interest in those ratios was motivated by a need to prove a crucial Claim stated in a recently proposed strongly polynomial-time algorithm for the general LP problem. That Claim is proved in this article and, as a consequence of this proof, a compact implementation of the strongly polynomial-time algorithm is suggested.

12 pages. Annotations have been added to make it more straightforward to review/read. This is a revised version of the article wherein the main lemma's proof is a proof by induction, instead of the direct proof that was used in the previous version of the article. This proof by induction is regarded by several reviewers as being clearer than the direct proof that it replaces