The Generalized Inverse in Linear Programming. Basic Structure

This paper considers the following linear programming problem: Maximize $( {x,c} )$ where $x \in \Lambda = \{ x| Ax = b,x\geqq \theta \}$. Duality is characterized in terms of orthogonality in n-space; edges and extreme points of $\Lambda $ are represented by certain eigenvectors; the problem is reformulated as a nonnegative fixed-point problem in $( {2n + 2} )$-space; and optimality is characterized in terms of the eigenvectors of $I - A^\dag A$, where $A^\dag $ is the (Moore–Penrose–Bjerhammar) generalized inverse of the $m \times n$ coefficient matrix A.