Linear constraint problem of Hermitian unitary symplectic matrices

ABSTRACT

In this paper, we consider a linear constraint problem of Hermitian unitary symplectic matrices and its approximation. By constructing a simple unitary matrix U, we verify that Hermitian unitary symplectic matrices are unitary similar to block diagonal Hermitian unitary matrices via U, which simplifies and is crucial to solving the linear constraint problem, and is a special feature of this paper. Then, we solve the linear constraint problem completely, that is deriving the sufficient and necessary conditions of it and inducing Hermitian unitary symplectic solutions to it. We also obtain its optimal approximate solutions. Furthermore, the Procrustes problem of Hermitian unitary symplectic matrices is considered when the linear constraint problem has no solution.

KEYWORDS:

• Hermitian unitary symplectic matrix
• linear constraint problem
• unitary similar
• optimal approximation

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 15A24
• 15B57
• 65F05

Acknowledgments

The author thanks the anonymous referees very much for their valuable suggestions and comments, which have greatly improved this manuscript.

Disclosure statement

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

Additional information

Funding

This research was supported by a Project Supported Scientific Research Fund of Department of Education of Zhejiang Province (Y201738285).