Hermitian pencils with a cubic minimal polynomial

DOI10.1016/0024-3795(82)90100-8zbMath0515.15005OpenAlexW1999800061MaRDI QIDQ1051708

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)90100-8

zbMATH Keywords

simultaneous reductioncubic minimal polynomialhermitian pencilsKippenhahn's conjectureunitarily similar to a block diagonal matrix

Mathematics Subject Classification ID

Matrices over function rings in one or more variables (15A54) Canonical forms, reductions, classification (15A21)

Related Items (7)

Equality of higher numerical ranges of matrices and a conjecture of Kippenhahn on Hermitian pencils ⋮ Indecomposable matrices defining plane cubics ⋮ 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 ⋮ A counterexample to Kippenhahn's conjecture on Hermitian pencils ⋮ Pencils of complex and real symmetric and skew matrices

Cites Work

• A weak property \(L\) for pairs of matrices
• Geometry of the numerical range of matrices
• On a conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two Hermitian matrices. I
• A conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two hermitian matrices. II
• A non-commutative spectral theorem
• Simultaneous block triangularization and block diagonalization of sets of matrices
• Pairs of Matrices With Property L. II
• On the Field of Values of a Square Matrix
• Über den Wertevorrat einer Matrix
• Pairs of Matrices with Property L

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