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Article Title

Eventual Cone Invariance

Keywords

Eventually nonnegative matrix, exponentially nonnegative matrix, Perron-Frobenius, proper cone

Abstract

Eventually nonnegative matrices are square matrices whose powers become and remain (entrywise) nonnegative. Using classical Perron-Frobenius theory for cone preserving maps, this notion is generalized to matrices whose powers eventually leave a proper cone K ⊂ R^n invariant, that is, A^mK ⊆ K for all sufficiently large m. Also studied are the related notions of eventual cone invariance by the matrix exponential, as well as other generalizations of M-matrix and dynamical system notions.

abs_vol32_pp204-216.pdf (115 kB)
Abstract in PDF

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