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

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:

• Inverse eigenvalue problem
• (skew) J-Hamiltonian matrix
• J-symplectic matrix
• Moore–Penrose inverse
• Procrustes problem

2000 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary: 15A09
• Secondary: 15A24

Acknowledgments

The authors thank the referees for their valuable comments and suggestions that allowed us to improve considerably the reading of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first and third authors were partially supported by Universidad de Buenos Aires, Argentina (EXP-UBA: 13.019/2017, 20020170100350BA). The third author is partially supported by Ministerio de Ciencia e Innovación of Spain (Grant Red de Excelencia RED2022-134176-T).