LINEAR MAPS PRESERVING THE LORENTZ SPECTRUM: THE 2 × 2 CASE

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Bueno M.I. (Author) Other; Susana Borges Furtado (Author) FEP; Klausmeier A. (Author) Other; Veltri J. (Author) Other

Journal

Title: Electronic Journal of Linear Algebra

Vol. 38

Pages: 317-330

ISSN: 15379582

Indexing

ISI Web of Science

Scopus - 2 Citations

Other information

Authenticus ID: P-00X-W6G

DOI: 10.13001/ela.2022.6925

Abstract (EN): In this paper, a complete description of the linear maps ¿: Wn ¿ Wn that preserve the Lorentz spectrum is given when n = 2, and Wn is the space Mn of n × n real matrices or the subspace Sn of Mn formed by the symmetric matrices. In both cases, it has been shown that ¿(A) = P AP¿1 for all A ¿ W2, where P is a matrix with a certain structure. It was also shown that such preservers do not change the nature of the Lorentz eigenvalues (that is, the fact that they are associated with Lorentz eigenvectors in the interior or on the boundary of the Lorentz cone). These results extend to n = 2 those for n ¿ 3 obtained by Bueno, Furtado, and Sivakumar (2021). The case n = 2 has some specificities, when compared to the case n ¿ 3, due to the fact that the Lorentz cone in R2 is polyedral, contrary to what happens when it is contained in Rn with n ¿ 3. Thus, the study of the Lorentz spectrum preservers on Wn = Mn also follows from the known description of the Pareto spectrum preservers on Mn.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13