In this paper we investigate the Sturmian theory for general (possibly uncontrollable) linear Hamiltonian systems by means of the Lidskii angles, which are associated with a symplectic fundamental matrix of the system. In particular, under the Legendre condition we derive formulas for the multiplicities of the left and right proper focal points of a conjoined basis of the system, as well as the Sturmian separation theorems for two conjoined bases of the system, in terms of the Lidskii angles. The results are new even in the completely controllable case. As the main tool we use the limit theorem for monotone matrix-valued functions by Kratz (1993). The methods allow to present a new proof of the known monotonicity property of the Lidskii angles. The results and methods can also be potentially applied in the singular Sturmian theory on unbounded intervals, in the oscillation theory of linear Hamiltonian systems without the Legendre condition, in the comparative index theory, or in linear algebra in the theory of matrices.

在本文中，我们通过 Lidskii 角研究一般（可能无法控制的）线性哈密顿系统的 Sturmian 理论，Lidskii 角与系统的辛基本矩阵相关联。特别地，在勒让德条件下，我们推导出系统的一个连体基的左、右真焦点的多重性公式，以及系统的两个连体基的 Sturmian 分离定理，根据 Lidskii 角. 即使在完全可控的情况下，结果也是新的。作为主要工具，我们使用 Kratz (1993) 的单调矩阵值函数的极限定理。这些方法允许提出对 Lidskii 角的已知单调性的新证明。