Results on the generalized numerical ranges in max algebra

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

Results on the generalized numerical ranges in max algebra

General Mathematics 2024-12-17 v1

Authors: Narges Haj Aboutalebi , Shaun Fallat , Aljosa Peperko , Davod Taghizadeh , Mohsen Zahraei

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.

Keywords

matrix rank hadamard matrices

Cite

@article{arxiv.2412.10375,
  title  = {Results on the generalized numerical ranges in max algebra},
  author = {Narges Haj Aboutalebi and Shaun Fallat and Aljosa Peperko and Davod Taghizadeh and Mohsen Zahraei},
  journal= {arXiv preprint arXiv:2412.10375},
  year   = {2024}
}

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23 pages, 2 figures

Results on the generalized numerical ranges in max algebra

Abstract

Keywords

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