A counterexample to Kippenhahn's conjecture on Hermitian pencils

DOI10.1016/0024-3795(83)90159-3zbMath0539.15004OpenAlexW1993304213WikidataQ123226987 ScholiaQ123226987MaRDI QIDQ793811

Thomas J. Laffey

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0024-3795(83)90159-3

zbMATH Keywords

Hermitian matricescounterexampleminimal polynomialnonderogatoryHermitian pencilssimultaneous reducibility

Mathematics Subject Classification ID

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

Related Items

Generating systems of the full matrix algebra that contain nonderogatory matrices ⋮ Geometry of free loci and factorization of noncommutative polynomials ⋮ Equality of higher numerical ranges of matrices and a conjecture of Kippenhahn on Hermitian pencils ⋮ Indecomposable matrices defining plane cubics ⋮ The Wigner distribution of n arbitrary observables ⋮ Determinantal hypersurfaces and representations of Coxeter groups ⋮ Free loci of matrix pencils and domains of noncommutative rational functions ⋮ 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 ⋮ Kippenhahn's Theorem for Joint Numerical Ranges and Quantum States ⋮ Pencils of complex and real symmetric and skew matrices

Cites Work

• Hermitian pencils with a cubic minimal polynomial
• A conjectured property of Hermitian pencils
• A conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two hermitian matrices. II
• Über den Wertevorrat einer Matrix
• Simultaneous similarity of matrices