Numerical range of linear pencils

DOI10.1016/S0024-3795(00)00145-2zbMath0966.15014MaRDI QIDQ1587893

Panayiotis J. Psarrakos

Publication date: 12 August 2001

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

zbMATH Keywords

eigenvaluenumerical rangeHermitian matrixboundarylinear pencilindefinite inner product spaceselfadjoint linear pencil

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Matrix pencils (15A22)

Related Items (23)

Fields of Values of Linear Pencils and Spectral Inclusion Regions ⋮ The Characteristic Polynomial of Linear Pencils of Small Size and the Numerical Range ⋮ \(A\)-numerical radius and product of semi-Hilbertian operators ⋮ Matrix Pencils with Coefficients that have Positive Semidefinite Hermitian Parts ⋮ Pseudospectra of Matrix Pencils for Transient Analysis of Differential-Algebraic Equations ⋮ Stability of matrix polynomials in one and several variables ⋮ Numerical solution of singular Sylvester equations ⋮ The ratio field of values ⋮ Compressions of linearly independent selfadjoint operators ⋮ Generalized Rayleigh quotients and generating vectors ⋮ Ratio numerical ranges of operators ⋮ Flat portions on the boundary of the indefinite numerical range of \(3\times 3\) matrices ⋮ The \(J\)-numerical range of a \(J\)-Hermitian matrix and related inequalities ⋮ Optimal quotients for solving large eigenvalue problems ⋮ On the relation of the Drazin inverse and matrix pencil theory methods for the study of generalized linear systems ⋮ Computing the numerical range of Krein space operators ⋮ Numerical approximation of the boundary of numerical range of matrix polynomials ⋮ On the shape of numerical range of matrix polynomials ⋮ The numerical range of linear pencils of 2-by-2 matrices ⋮ Indefinite numerical range of 3 × 3 matrices ⋮ \(J\)-orthostochastic matrices of size \(3 \times 3\) and numerical ranges of Krein space operators ⋮ Matrix pencils with the numerical range equal to the whole complex plane ⋮ Definite triples of Hermitian matrices and matrix polynomials

Cites Work

• Inertia characteristics of self-adjoint matrix polynomials
• Geometry of the numerical range of matrices
• A conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two hermitian matrices. II
• The boundary of the numerical range of matrix polynomials
• An Extension of the Hausdorff-Toeplitz Theorem on the Numerical Range
• Numerical Range of Matrix Polynomials
• Remarks on numerical ranges of operators in spaces with an indefinite metric
• Shapes and computer generation of numerical ranges of Krein space operators
• Numerical ranges of an operator on an indefinite inner product space
• Über den Wertevorrat einer Matrix
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