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@article{1762097, author = {Šepitka, Peter and Šimon Hilscher, Roman}, article_number = {September}, doi = {http://dx.doi.org/10.1016/j.laa.2021.04.012}, keywords = {Comparative index; Dual comparative index; Lidskii angle; Argument of symplectic matrix; Conjoined basis; Lagrangian subspace}, language = {eng}, issn = {0024-3795}, journal = {Linear Algebra and its Applications}, title = {Comparative index and Lidskii angles for symplectic matrices}, url = {https://www.sciencedirect.com/science/article/pii/S0024379521001695#!}, volume = {624}, year = {2021} }
TY - JOUR ID - 1762097 AU - Šepitka, Peter - Šimon Hilscher, Roman PY - 2021 TI - Comparative index and Lidskii angles for symplectic matrices JF - Linear Algebra and its Applications VL - 624 IS - September SP - 174-197 EP - 174-197 PB - Elsevier SN - 00243795 KW - Comparative index KW - Dual comparative index KW - Lidskii angle KW - Argument of symplectic matrix KW - Conjoined basis KW - Lagrangian subspace UR - https://www.sciencedirect.com/science/article/pii/S0024379521001695#! N2 - In this paper we establish a connection between two important concepts from the matrix analysis, which have fundamental applications in the oscillation theory of differential equations. These are the traditional Lidskii angles for symplectic matrices and the recently introduced comparative index for a pair of Lagrangian planes. We show that the comparative index can be calculated by a specific argument function of symplectic orthogonal matrices, which are constructed from the Lagrangian planes. The proof is based on a topological property of the symplectic group and on the Sturmian separation theorem for completely controllable linear Hamiltonian systems. We apply the main result in order to present elegant proofs of certain important properties of the comparative index. ER -
ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Comparative index and Lidskii angles for symplectic matrices. \textit{Linear Algebra and its Applications}. Elsevier, 2021, roč.~624, September, s.~174-197. ISSN~0024-3795. Dostupné z: https://dx.doi.org/10.1016/j.laa.2021.04.012.
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