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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this entry
Cite this entry
Gass, S.I., Harris, C.M. (2001). Transposition theorems . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_1066
Download citation
DOI: https://doi.org/10.1007/1-4020-0611-X_1066
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-7923-7827-3
Online ISBN: 978-1-4020-0611-1
eBook Packages: Springer Book Archive