An algebraic approach to the construction of polyhedral invariant cones

In this paper, based on algebraic arguments, a newpro of of the spectral characterization of those real matrices that leave a proper polyhedral cone invariant [Trans. Amer. Math. Soc., 343 (1994), pp. 479–524] is given. The proof is a constructive one, as it allows us to explicitly obtain for every matrix A, which satisfies the aforementioned spectral requirements, an A-invariant proper polyhedral cone K. Some newresults are also presented, concerning the way A acts on the cone K. In particular, K-irreducibility, K-primitivity, and K-positivity are fully characterized.