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.

摘要

在本文中，我们考虑了 Hermitian 酉辛矩阵的线性约束问题及其逼近。通过构造一个简单的酉矩阵U ，我们通过U验证了 Hermitian 酉辛矩阵与块对角 Hermitian 酉矩阵相似，这简化了线性约束问题并且对解决线性约束问题至关重要，并且是本文的一个特点。然后，我们完全解决了线性约束问题，即推导它的充分必要条件，并推导出它的Hermitian酉辛解。我们也得到了它的最优近似解。此外，当线性约束问题无解时，考虑Hermitian酉辛矩阵的Procrustes问题。