An algebraic approach to the construction of polyhedral invariant cones

In this paper, based on algebraic arguments, a new proof of the spectral ch aracterization of those real matrices that leave a proper polyhedral cone i nvariant [ 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 satis es the aforementioned spectral requirements, an A-in variant proper polyhedral cone K. Some new results are also presented, concerning the way A acts on the cone K. In particular, K-irreducibility, K-primitivity, and K-positivity are ful ly characterized.