Zero polyhedral cones (Q1431847)

This short article presents some interesting properties of zero polyhedral cones. The main part of the article is split into two sections. In the first section the main result is presented and proven, namely that the statements \(P^+(A)=\{0\}\), \(P^+(B^k)=\{0\}\) and \(P^+(B)=\{0\}\) are equivalent, where matrix \(B\) is a Fourier-Motzkin elimination of \(A\). In the second section, two algorithms (based on the main result of the article) to check if a polyhedral cone \(P(T)\) is zero are presented.