Inequalities for \(J\)-Hermitian matrices

DOI10.1016/j.laa.2005.05.021zbMath1091.15024OpenAlexW2108099383MaRDI QIDQ2568390

Hiroshi Nakazato, Rute Lemos, Natália Bebiano, Graça Soares, João da Providência

Publication date: 10 October 2005

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2005.05.021

zbMATH Keywords

inequalities involving eigenvaluesindefinite inner product\(J\)-Hermitian matrixRayleigh-Ritz theoremKy Fan maximum principle\(J,C\)-numerical rangeSchur's majorization theorem

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20)

Related Items (12)

Log-majorization Type Inequalities ⋮ The \(J\)-numerical range of a \(J\)-Hermitian matrix and related inequalities ⋮ Computing the numerical range of Krein space operators ⋮ Trace inequalities for logarithms and powers of J-Hermitian matrices ⋮ An inverse indefinite numerical range problem ⋮ Analogs of Cauchy-Poincaré and Fan-Pall interlacing theorems for \(J\)-Hermitian and \(J\)-normal matrices ⋮ More on geometry of Krein space \(C\)-numerical range ⋮ The boundary of the Krein space tracial numerical range, an algebraic approach and a numerical algorithm ⋮ Indefinite higher-rank numerical ranges ⋮ On the Courant--Fischer theory for Krein spaces ⋮ The numerical range of banded 2-Toeplitz operators in spaces with an indefinite metric ⋮ \(J\)-orthostochastic matrices of size \(3 \times 3\) and numerical ranges of Krein space operators

Cites Work

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• Elementary inclusion relations for generalized numerical ranges
• Löwner inequality of indefinite type
• Zur Abschätzung von Matrizennormen
• Matrix Analysis
• An inequality for the trace of the product of two symmetric matrices
• On Generalized Numerical Ranges of Operators on an Indefinite Inner Product Space
• On the Trace of Matrix Products
• Inequalities: theory of majorization and its applications

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