Another Proof of the Fact that Polyhedral Cones are Finitely Generated

Details Another Proof of the Fact that Polyhedral Cones are Finitely Generated Another Proof of the Fact that Polyhedral Cones are Finitely Generated

2009-12-15

arxiv.org/abs/0912.2927v1

Mathematics

Combinatorics

5 pages, 3 figures

Scientific paper

In this note, we work out a simple inductive proof showing that every polyhedral cone K is the conic hull of a finite set X of vectors. The base cases of the induction are linear subspaces and linear halfspaces of linear subspaces. The proof also shows that the components of the vectors in X can be chosen (up to their sign) to be quotients of subdeterminants of the coefficient matrix of any inequality system defining K.

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