The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.
@article{bwmeta1.element.bwnjournal-article-zmv22z2p145bwm,
author = {Jan Hauke and Augustyn Markiewicz},
title = {On orderings induced by the Loewner partial ordering},
journal = {Applicationes Mathematicae},
volume = {22},
year = {1994},
pages = {145-154},
zbl = {0840.15014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv22z2p145bwm}
}
Hauke, Jan; Markiewicz, Augustyn. On orderings induced by the Loewner partial ordering. Applicationes Mathematicae, Tome 22 (1994) pp. 145-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv22z2p145bwm/
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