The higher rank numerical range of matrix polynomials

2011/04/07 by Aikaterini Aretaki, Aretaki, Aikaterini, John Maroulas +1
Computer Science · Mathematics · #15A60 #15A90 #81P68 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1104.1341

openalex publication_date 2011/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The notion of the higher rank numerical range Λ_k(L(λ)) for matrix polynomials L(λ)=A_mλ^m+...+A₁λ+A₀ is introduced here and some fundamental geometrical properties are investigated. Further, the sharp points of Λ_k(L(λ)) are defined and their relation to the numerical range w(L(λ)) is presented. A connection of Λ_k(L(λ)) with the vector-valued higher rank numerical range Λ_k(A₀,..., A_m) is also discussed.

Citations

• Quantum error correction and generalized numerical ranges

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