Title: A Dual Characterization of the Ye's Condition Number

In this work we study the Ye's condition number defined in [1], which is based on the size of the large variables on the optimal set of the linear programming problem. We prove that this number coincides with the minimum inner product of the cost vector with the extremal feasible directions from the optimal set. The demonstration relies on dual properties of the problem defining the Ye's condition measure. [1] Y. Ye. On the finite convergence of interior-point algorithms for linear programming. Mathematical Programming, 57 (1992), 325-335.