ABSTRACT

We obtain several analogs of real polar decomposition for even dimensional matrices. In particular, we decompose a non-degenerate matrix as a product of a Hamiltonian and an anti-symplectic matrix and under additional requirements we decompose a matrix as a skew-Hamiltonian and a symplectic matrix. We apply our results to study bosonic Gaussian channels up to inhomogeneous symplectic transforms.

中文翻译：

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极性分解的辛类比及其在玻色子高斯通道中的应用

摘要

我们获得了偶数维矩阵的几个实极分解的类似物。特别是，我们将非退化矩阵分解为哈密顿矩阵和反辛矩阵的乘积，并且在附加要求下，我们将矩阵分解为斜哈密顿矩阵和辛矩阵。我们将我们的结果应用于研究玻色子高斯通道直至非均匀辛变换。