An Algebraic Approach to the Construction of Polyhedral Invariant Cones
Maria Elena Valcher, Lorenzo Farina · SIAM Journal on Matrix Analysis and Applications · 2000
In this paper, based on algebraic arguments, a new proof 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 $\mathcal{K}$. Some new results are also presented, concerning the way A acts on the cone $\mathcal{K}$. In particular, $\mathcal{K}$-irreducibility, $\mathcal{K}$-primitivity, and $\mathcal{K}$-positivity are fully characterized.