Linear constraint problem of Hermitian unitary symplectic matrices

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 simplif...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 70; no. 8; pp. 1423 - 1441
Main Author Zhao, Lijun
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 24.05.2022
Taylor & Francis Ltd
Subjects
Hermitian unitary symplectic matrix
linear constraint problem
Mathematical analysis
optimal approximation
unitary similar
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Summary: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.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2020.1762533