A generalization of spectral radius, numerical radius, and spectral norm
type: Item
instance of: scholarly article
title: A generalization of spectral radius, numerical radius, and spectral norm
zbMATH Open document ID: 0624.15012
DOI: 10.1016/0024-3795(87)90309-0
author: Chikwong Li
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: The author defines three quantities, \(\rho\) (A), r(A), and \(\| A\|\), as scalar functions of a matrix A. These are \(\ell_ p\) norms of tuples formed respectively from the eigenvalues of A, the diagonal of a unitary similarity of A (that is, \(UAU^*)\), and the diagonal of a matrix unitarily equivalent to A (that is, UAV), where U, V are to be unitary. In the second and third possibilities, r and \(\| \cdot \|\) are the maximum of the specified \(\ell_ p\) norms as U and V vary over all unitary matrices. The author studies those matrices A for which equalities exist among \(\rho\) (A), r(A), and \(\| A\|\). Furthermore, the norm properties of r(A) and \(\| A\|\) are investigated.
reviewed by: Robert C. Thompson
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 4012825
zbMATH Keywords: numerical range
zbMATH Keywords: spectral radius
zbMATH Keywords: spectral norm
zbMATH Keywords: \(\ell p\)-norm
zbMATH Keywords: unitary similarity
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90309-0
OpenAlex ID: W2019170085
cites work: Interpolation zwischen den Klassen 𝔖p von Operatoren in Hilberträumen
cites work: On certain finite dimensional numerical ranges and numerical radii†
cites work: Operator norms, multiplicativity factors, and C-numerical radii
cites work: Q5521075
cites work: The generalized spectral radius, numerical radius and spectral norm
cites work: Unitarily invariant generalized matrix norms and hadamard products
cites work: On the Field of Values of a Square Matrix
cites work: The generalizedK- numerical range
cites work: Norms and the spectral radius of matrices
cites work: Singular Values, Diagonal Elements, and Convexity
cites work: On the shape of the generalized numerical ranges
description: scientific article; zbMATH DE number 4012825