Další formáty:
BibTeX
LaTeX
RIS
@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, roč.~624, September, s.~174-197. ISSN~0024-3795. doi:10.1016/j.laa.2021.04.012. 2021.
|
