Reduction to generalized Hessenberg form and inverse spectral problems

DOI10.1016/0024-3795(92)90230-8zbMath0757.15004OpenAlexW1996453516MaRDI QIDQ1184474

Leonid Faybusovich

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1016/0024-3795(92)90230-8

zbMATH Keywords

inverse spectral problemsemisimple Lie algebrassimilarity transformsgeneralized Hessenberg formsymmetric generalized Hessenberg matrices

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Simple, semisimple, reductive (super)algebras (17B20) Direct numerical methods for linear systems and matrix inversion (65F05) Canonical forms, reductions, classification (15A21)

Cites Work

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• On Hamiltonian and symplectic Hessenberg forms
• On symmetric rational transfer functions
• The QR-algorithm and generalized Toda flows
• The geometry of matrix eigenvalue methods
• Generalized Eulerian numbers and the topology of the Hessenberg variety of a matrix
• Self-similar flows
• QR-type factorizations, the Yang-Baxter equation, and an eigenvalue problem of control theory
• The solution to a generalized Toda lattice and representation theory
• Matrix factorizations for symplectic QR-like methods
• A Hamiltonian $QR$ Algorithm
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system

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