Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Transposition theorems

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_1066

Transposition theorems deal with disjoint alternatives of solvability of linear systems. For example, the transportation theorem of Stiemke is: For a matrix Av ≠ 0, the following statements are equivalent: (1) Axv = 0, xv > 0, has no solution, and (2) μAv ≤ 0, μAv ≠ 0 has a solution. Farkas' lemma; Gordan's theorem; Strong duality theorem; Theorem of alternatives.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA