Naslov
Monotone transformations on the cone of all positive semidefinite real matrices

Autori
Golubić, Iva ; Marovt, Janko

Izvornik
Mathematica slovaca (0139-9918) 70 (2020); 733-744

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
preserver ; symmetric matrix ; star partial order ; minus partial order ; Löwner partial order

Sažetak
Let Hn+(R) be the cone of all positive semidefinite (symmetric) n × n real matrices. Matrices from Hn+(R) play an important role in many areas of engineering, applied mathematics, and statistics, e.g. every variance-covariance matrix is known to be positive semidefinite and every real positive semidefinite matrix is a variance-covariance matrix of some multivariate distribution. Three of the best known partial orders that were mostly studied on various sets of matrices are the Löwner, the minus, and the star partial orders. Motivated by applications in statistics authors have recently investigated the form of maps on Hn+(R) that preserve either the Löwner or the minus partial order in both directions. In this paper we continue with the study of preservers of partial orders on Hn+(R). We characterize surjective, additive maps on Hn+ (R), n ≥ 3, that preserve the star partial order in both directions. We also investigate the form of surjective maps on the set of all symmetric real n × n matrices that preserve the Löwner partial order in both directions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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