On the shape of numerical range of matrix polynomials

DOI10.1016/S0024-3795(01)00374-3zbMath0996.15018OpenAlexW2071417418WikidataQ127586916 ScholiaQ127586916MaRDI QIDQ5955651

Hiroshi Nakazato, Panayiotis J. Psarrakos

Publication date: 11 April 2002

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(01)00374-3

zbMATH Keywords

numerical rangematrix polynomialmatrix pencil

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12) Matrices over function rings in one or more variables (15A54)

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Birkhoff-James \(\varepsilon\)-orthogonality sets of vectors and vector-valued polynomials ⋮ On the Stability Radius of Matrix Polynomials ⋮ Self-inversive Hilbert space operator polynomials with spectrum on the unit circle ⋮ The Characteristic Polynomial of Linear Pencils of Small Size and the Numerical Range ⋮ On a Compression of Normal Matrix Polynomials ⋮ The ratio field of values ⋮ Compressions of linearly independent selfadjoint operators ⋮ Birkhoff-James approximate orthogonality sets and numerical ranges ⋮ Ratio numerical ranges of operators ⋮ Unnamed Item ⋮ On theq-numerical range of matrices and matrix polynomials ⋮ The Toeplitz-Hausdorff theorem revisited: Relating linear algebra and geometry ⋮ Numerical approximation of the boundary of numerical range of matrix polynomials ⋮ Indefinite numerical range of 3 × 3 matrices ⋮ The block numerical range of matrix polynomials ⋮ Polynomial numerical hulls of matrix polynomials ⋮ Matrix pencils with the numerical range equal to the whole complex plane ⋮ On the Numerical Range of Operator Polynomials ⋮ Point equation of the boundary of the numerical range of a matrix polynomial

Cites Work

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• Inertia characteristics of self-adjoint matrix polynomials
• The boundary of the numerical range of matrix polynomials
• Numerical range of linear pencils
• Numerical Range of Matrix Polynomials
• Compressions and Dilations of Numerical Ranges
• Numerical ranges of an operator on an indefinite inner product space
• On the relation between the numerical range and the joint numerical range of matrix polynomials
• Normal and seminormal eigenvalues of matrix functions
• The numerical range of linear pencils of 2-by-2 matrices

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