Procrustes problem for the inverse eigenvalue problem of normal (skew) $J$-Hamiltonian matrices and normal $J$-symplectic matrices

S. Gigola; L. Lebtahi; N. Thome

Procrustes problem for the inverse eigenvalue problem of normal (skew) $J$-Hamiltonian matrices and normal $J$-symplectic matrices

Optimization and Control 2024-01-25 v1

Authors: S. Gigola , L. Lebtahi , N. Thome

Abstract

A square complex matrix $A$ is called (skew) $J$ -Hamiltonian if $AJ$ is (skew) hermitian where $J$ is a real normal matrix such that $J^2=-I$ , where $I$ is the identity matrix. In this paper, we solve the Procrustes problem to find normal (skew) $J$ -Hamiltonian solutions for the inverse eigenvalue problem. In addition, a similar problem is investigated for normal $J$ -symplectic matrices.

Keywords

Procrustes problem inverse eigenvalue problem normal skew J-Hamiltonian matrices normal J-symplectic matrices matrix decomposition

Cite

@article{arxiv.2401.13121,
  title  = {Procrustes problem for the inverse eigenvalue problem of normal (skew) $J$-Hamiltonian matrices and normal $J$-symplectic matrices},
  author = {S. Gigola and L. Lebtahi and N. Thome},
  journal= {arXiv preprint arXiv:2401.13121},
  year   = {2024}
}

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25 pages

Procrustes problem for the inverse eigenvalue problem of normal (skew) $J$-Hamiltonian matrices and normal $J$-symplectic matrices

Abstract

Keywords

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