On a conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two Hermitian matrices. I

DOI10.1016/0024-3795(82)90254-3zbMath0487.15006OpenAlexW4241456579WikidataQ123269210 ScholiaQ123269210MaRDI QIDQ1165292

Helene Shapiro

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0024-3795(82)90254-3

zbMATH Keywords

Hermitian matricesinvariant subspacecharacteristic polynomialcommon eigenvectorunitary similaritypencil of matricesKippenhahn's conjecturereducability

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Hermitian, skew-Hermitian, and related matrices (15B57) Matrices over function rings in one or more variables (15A54) Canonical forms, reductions, classification (15A21)

Related Items (10)

On Generalized Numerical Ranges of Operators on an Indefinite Inner Product Space ⋮ Equality of higher numerical ranges of matrices and a conjecture of Kippenhahn on Hermitian pencils ⋮ Indecomposable matrices defining plane cubics ⋮ A conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two hermitian matrices. II ⋮ Singularities of base polynomials and Gau-Wu numbers ⋮ Burnside graphs, algebras generated by sets of matrices, and the Kippenhahn conjecture ⋮ Examples for the quantum Kippenhahn theorem ⋮ A survey of canonical forms and invariants for unitary similarity ⋮ Hermitian pencils with a cubic minimal polynomial ⋮ A conjectured property of Hermitian pencils

Cites Work

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• A non-commutative spectral theorem
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• Pairs of Matrices With Property L. II
• Commutativity in Finite Matrices
• On the Field of Values of a Square Matrix
• On the characteristic roots of matric polynomials
• Some Theorems on Commutative Matrices
• Über den Wertevorrat einer Matrix
• Pairs of Matrices with Property L
• A Note on Pairs of Normal Matrices with Property L
• Pairs of normal matrices with property L

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