Preservers of partial orders on the set of all variance-covariance matrices
Filomat, Tome 34 (2020) no. 9, p. 3015
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Let H + n (R) be the cone of all positive semidefinite n × n real matrices. Two of the best known partial orders that were mostly studied on subsets of square complex matrices are the Löwner and the minus partial orders. Motivated by applications in statistics we study these partial orders on H + n (R). We describe the form of all surjective maps on H + n (R), n > 1, that preserve the Löwner partial order in both directions. We present an equivalent definition of the minus partial order on H + n (R) and also characterize all surjective, additive maps on H + n (R), n ≥ 3, that preserve the minus partial order in both directions.
Classification :
15B48, 15A86, 47L07, 47B49, 54F05, 62J99
Keywords: linear model, preserver, Löwner partial order, minus partial order, variance-covariance matrix
Keywords: linear model, preserver, Löwner partial order, minus partial order, variance-covariance matrix
Iva Golubić; Janko Marovt. Preservers of partial orders on the set of all variance-covariance matrices. Filomat, Tome 34 (2020) no. 9, p. 3015 . doi: 10.2298/FIL2009015G
@article{10_2298_FIL2009015G,
author = {Iva Golubi\'c and Janko Marovt},
title = {Preservers of partial orders on the set of all variance-covariance matrices},
journal = {Filomat},
pages = {3015 },
year = {2020},
volume = {34},
number = {9},
doi = {10.2298/FIL2009015G},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2009015G/}
}
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