A Jacobi Algorithm in Phase Space: Diagonalizing (skew-) Hamiltonian and Symplectic Matrices with Dirac-Majorana Matrices
Mathematical Physics
2021-05-19 v2 math.MP
Abstract
Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report about the generalization of these elementary rotations towards canonical transformations acting in Hamiltonian phase spaces. This generalization allows to use Jacobi's method in order to compute eigenvalues and eigenvectors of Hamiltonian (and skew-Hamiltonian) matrices with either purely real or purely imaginary eigenvalues by successive elementary symplectic "decoupling"-transformations.
Keywords
Cite
@article{arxiv.2008.13409,
title = {A Jacobi Algorithm in Phase Space: Diagonalizing (skew-) Hamiltonian and Symplectic Matrices with Dirac-Majorana Matrices},
author = {Christian Baumgarten},
journal= {arXiv preprint arXiv:2008.13409},
year = {2021}
}
Comments
Some typos corrected