2022/12/01 by Emanuel Malvetti, Gunther Dirr, Malvetti, Emanuel +5
Computer Science · Mathematics · #15A20 (Primary) 17B20 (Secondary) #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2212.00713
openalex publication_date 2022/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix diagonalization, such as the eigenvalue decomposition of real symmetric or complex Hermitian matrices, and the real or complex singular value decomposition. Concretely, given a path of structured matrices with a certain smoothness, we study what kind of smoothness one can obtain for the corresponding diagonalization of the matrices.