A conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two hermitian matrices. II

DOI10.1016/0024-3795(82)90212-9zbMath0495.15007OpenAlexW2051925191WikidataQ122963394 ScholiaQ122963394MaRDI QIDQ1169533

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)90212-9

zbMATH Keywords

reducibilitycharacteristic polynomialhermitian matricesblock diagonal matrixpencil

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Canonical forms, reductions, classification (15A21)

Related Items (16)

The Characteristic Polynomial of Linear Pencils of Small Size and the Numerical Range ⋮ On Matrices with Elliptical Numerical Ranges ⋮ 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 ⋮ The numerical range of \(3 \times 3\) matrices ⋮ On the geometry of numerical ranges in spaces with an indefinite inner product ⋮ Burnside graphs, algebras generated by sets of matrices, and the Kippenhahn conjecture ⋮ Indefinite numerical range of 3 × 3 matrices ⋮ Examples for the quantum Kippenhahn theorem ⋮ A survey of canonical forms and invariants for unitary similarity ⋮ Non-parallel Flat Portions on the Boundaries of Numerical Ranges of 4-by-4 Nilpotent Matrices ⋮ Hermitian pencils with a cubic minimal polynomial ⋮ Numerical range of linear pencils ⋮ A counterexample to Kippenhahn's conjecture on Hermitian pencils ⋮ Pencils of complex and real symmetric and skew matrices ⋮ Perron-Frobenius type results on the numerical range

Cites Work

• On the numerical range of a bounded operator
• Pairs of matrices with quadratic minimal polynomials
• On a conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two Hermitian matrices. I
• Normality and the numerical range
• Simultaneous block triangularization and block diagonalization of sets of matrices
• Field Convexity of a Square Matrix
• Pairs of Matrices With Property L. II
• Alternative proofs of a theorem of Moyls and Marcus on the numerical range of a square matrix
• On the Field of Values of a Square Matrix
• Über den Wertevorrat einer Matrix
• Pairs of Matrices with Property L
• Unnamed Item
• Unnamed Item
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