English

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

R2 v1 2026-06-23T18:12:07.406Z