Linear algebra meets Lie algebra: the Kostant-Wallach theory
Noam Shomron, Beresford N. Parlett
TL;DR
This paper explores the intersection of linear algebra and Lie algebra through Kostant and Wallach's results on matrix fibers with specified eigenvalues, also introducing related algebraic geometry and integrable systems concepts.
Contribution
It provides a dual-language exposition of Kostant and Wallach's results and offers an accessible introduction to related advanced mathematical topics.
Findings
Characterization of matrix fibers with prescribed eigenvalues
Connection between linear algebra and Lie algebra structures
Introduction to algebraic geometry and integrable systems concepts
Abstract
In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Geometry