In order to use the Dual Simplex Method, one needs to prove a certain bijection between the dictionaries associated with the primal problem and those associated with its dual. We give a short conceptual proof of why this bijection exists.
Cite
@article{arxiv.2310.02268,
title = {Dual Dictionaries in Linear Programming},
author = {Patrick T. Perkins and Xiang Gao},
journal= {arXiv preprint arXiv:2310.02268},
year = {2023}
}