Comparative index and Lidskii angles for symplectic matrices
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00118938" target="_blank" >RIV/00216224:14310/21:00118938 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0024379521001695#" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0024379521001695#</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2021.04.012" target="_blank" >10.1016/j.laa.2021.04.012</a>
Alternative languages
Result language
angličtina
Original language name
Comparative index and Lidskii angles for symplectic matrices
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA19-01246S" target="_blank" >GA19-01246S: New oscillation theory for linear Hamiltonian and symplectic systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and its Applications
ISSN
0024-3795
e-ISSN
—
Volume of the periodical
624
Issue of the periodical within the volume
September
Country of publishing house
US - UNITED STATES
Number of pages
24
Pages from-to
174-197
UT code for WoS article
000648525400010
EID of the result in the Scopus database
2-s2.0-85104377969