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Journal of Convex Analysis 26 (2019), No. 3, 1021--1052
Copyright Heldermann Verlag 2019



Multicones, Duality and Matrix Invariance

Michela Brundu
Dip. di Matematica e Geoscienze, UniversitÓ di Trieste, 34127 Trieste, Italy
brundu@units.it

Marino Zennaro
Dip. di Matematica e Geoscienze, UniversitÓ di Trieste, 34127 Trieste, Italy
zennaro@units.it



We analyze the geometric structure and properties of a certain class of subsets of Rd, here called multicones, which are natural generalizations of the classical cones. For them we introduce and investigate a suitable extension of the concept of duality, which allows us to treat in a convenient way many issues related to their invariance and strict invariance for real matrices.

Keywords: Cone, multicone, duality, matrix, invariant set, leading eigenvalue, leading eigenvector.

MSC: 15A18, 15A48, 52A30, 52B55.

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