Linear algebra meets Lie algebra: the Kostant-Wallach theory

DOI10.1016/j.laa.2009.06.007zbMath1227.15012arXiv0809.1204OpenAlexW2963617560WikidataQ115344861 ScholiaQ115344861MaRDI QIDQ732065

Beresford N. Parlett, Noam Shomron

Publication date: 9 October 2009

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

Full work available at URL: https://arxiv.org/abs/0809.1204

zbMATH Keywords

integrable systemscontrol theoryRitz valuesPoisson manifoldsgroup actions on varietiesHessenberg matricesGelfand-Zeitlin group

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Inverse problems in linear algebra (15A29) Canonical forms, reductions, classification (15A21)

Cites Work

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• Gelfand-Zeitlin actions and rational maps
• The Gelfand-Cetlin system and quantization of the complex flag manifolds
• Principal minors and diagonal similarity of matrices
• Polynomial relations among principal minors of a \(4\times 4\)-matrix
• Matrices with prescribed Ritz values
• Action-angle Coordinates for Integrable Systems on Poisson Manifolds
• Integrable geodesic flows on homogeneous spaces
• Introduction to Classical Integrable Systems

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