| dc.creator | Antezana, Jorge Abel | |
| dc.creator | Ghiglioni, Eduardo Mario | |
| dc.creator | Stojanoff, Demetrio | |
| dc.date | 2020 | |
| dc.date | 2021-10-14T18:27:05Z | |
| dc.date.accessioned | 2023-07-15T03:13:26Z | |
| dc.date.available | 2023-07-15T03:13:26Z | |
| dc.identifier | http://sedici.unlp.edu.ar/handle/10915/126676 | |
| dc.identifier | issn:0022-247x | |
| dc.identifier | issn:1096-0813 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/7464898 | |
| dc.description | Abstract Consider the Lie group of n × n complex unitary matrices U ( n ) endowed with the bi-invariant Finsler metric given by the spectral norm, ‖ X ‖ U = ‖ U ⁎ X ‖ ∞ = ‖ X ‖ ∞ for any X tangent to a unitary operator U. Given two points in U ( n ) , in general there exist infinitely many curves of minimal length. In this paper we provide a complete description of such curves and as a consequence we give an equivalent condition for uniqueness. Similar studies are done for the Grassmann manifolds. On the other hand, consider the cone of n × n positive invertible matrices G l ( n ) + endowed with the bi-invariant Finsler metric given by the trace norm, ‖ X ‖ 1 , A = ‖ A − 1 / 2 X A − 1 / 2 ‖ 1 for any X tangent to A ∈ G l ( n ) + . In this context, also exist infinitely many curves of minimal length. In this paper we provide a complete description of such curves proving first a characterization of the minimal curves joining two Hermitian matrices X , Y ∈ H ( n ) . The last description is also used to construct minimal paths in the group of unitary matrices U ( n ) endowed with the bi-invariant Finsler metric ‖ X ‖ 1 , U = ‖ U ⁎ X ‖ 1 = ‖ X ‖ 1 for any X tangent to U ∈ U ( n ) . We also study the set of intermediate points in all the previous contexts. | |
| dc.description | Departamento de Matemática | |
| dc.format | application/pdf | |
| dc.language | en | |
| dc.rights | http://creativecommons.org/licenses/by-nc-sa/4.0/ | |
| dc.rights | Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) | |
| dc.subject | Matemática | |
| dc.subject | Combinatorics | |
| dc.subject | Grassmannian | |
| dc.subject | Lie group | |
| dc.subject | Unitary operator | |
| dc.subject | Trace (linear algebra) | |
| dc.subject | Mathematics | |
| dc.subject | Matrix norm | |
| dc.subject | Hermitian matrix | |
| dc.subject | Unitary matrix | |
| dc.title | Minimal curves in U(n) and Gl(n)+ with respect to the spectral and the trace norms | |
| dc.type | Articulo | |
| dc.type | Preprint | |
