Results on the generalized numerical ranges in max algebra

Narges Haj Aboutalebi; Shaun Fallat; Aljosa Peperko; Davod Taghizadeh; Mohsen Zahraei

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arXiv · 2412.10375

Results on the generalized numerical ranges in max algebra

Narges Haj Aboutalebi·Shaun Fallat·Aljosa Peperko·Davod Taghizadeh·Mohsen Zahraei

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Abstract

Let $n$ and $k$ be two positive integers with $k\leq n$ and $C$ an $n \times n$ matrix with nonnegative entries. In this paper, the rank-$k$ numerical range in the max algebra setting is introduced and studied. The related notions of the max joint $k$-numerical range and the max joint $C$-numerical range of an entry-wise nonnegative matrix and an $m$-tuple of nonnegative matrices are also introduced. Some interesting algebraic properties of these concepts are investigated.

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Narges Haj Aboutalebi, Shaun Fallat, Aljosa Peperko, Davod Taghizadeh, Mohsen Zahraei. 2024-11-20. Results on the generalized numerical ranges in max algebra. https://arxiv.org/abs/2412.10375

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