The generalized spectral matrices and radial matrices on symmetry classes of tensors
type: Item
instance of: scholarly article
title: The generalized spectral matrices and radial matrices on symmetry classes of tensors
zbMATH Open document ID: 0612.15020
DOI: 10.1016/0024-3795(87)90206-0
author: Tin-Yau Tam
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: By using the m-th tensor power of \({\mathbb{C}}^ n\) and two fixed matrices A and C, the author defines three quantities generalizing the norm, the numerical radius and the spectral radius. After establishing the general inequalities between them he then studies operators for which equalities occur. The results involve various conditions on A, C, their eigenvalues and singular values.
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 3989575
zbMATH Keywords: tensor power
zbMATH Keywords: norm
zbMATH Keywords: numerical radius
zbMATH Keywords: spectral radius
zbMATH Keywords: inequalities
zbMATH Keywords: eigenvalues
zbMATH Keywords: singular values
reviewed by: Jaroslav Zemánek
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90206-0
OpenAlex ID: W2073504731
cites work: Weyl's inequality and quadratic forms on the Grassmannian
cites work: On the numerical range of an operator
cites work: A characterization of spectraloid operators and its generalization
cites work: Q3291799
cites work: On certain finite dimensional numerical ranges and numerical radii†
cites work: Elementary inclusion relations for generalized numerical ranges
cites work: The numerical radius and specttural matrices
cites work: On matrices having equal spectral radius and spectral norm
cites work: On the Singular Values of a Product of Completely Continuous Operators
cites work: On the Eigenvalues of a Matrix with Prescribed Singular Values
cites work: Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix
cites work: The decomposable numerical radius and numerical radius of a compound matrix
cites work: The generalized spectral radius, numerical radius and spectral norm
cites work: Q4771383
cites work: The numerical radius of exterior powers
cites work: On the Field of Values of a Square Matrix
cites work: Isometric parts of operators and the critical exponent
cites work: Induced operators on symmetry classes of tensors
cites work: On the generalized radial matrices and a conjecture of Marcus and Sandy
cites work: Inequalities between the Two Kinds of Eigenvalues of a Linear Transformation
description: scientific article; zbMATH DE number 3989575