2020/08/31 by C. Baumgarten, Baumgarten, Christian
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2008.13409
openalex publication_date 2020/08/31 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Jacobi's method is a well-known algorithm in linear algebra to diagonalize\nsymmetric matrices by successive elementary rotations. We report about the\ngeneralization of these elementary rotations towards canonical transformations\nacting in Hamiltonian phase spaces. This generalization allows to use Jacobi's\nmethod in order to compute eigenvalues and eigenvectors of Hamiltonian (and\nskew-Hamiltonian) matrices with either purely real or purely imaginary\neigenvalues by successive elementary symplectic "decoupling"-transformations.\n