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 SM ISO690:2012LAWSON, Jimmie, LIM, Yongdo. Geometric means and re ection quasigroups
. In: Quasigroups and Related Systems, 2006, vol. 14, nr. 1(15), pp. 43-59. ISSN 1561-2848. |
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| Quasigroups and Related Systems | ||||||
| Volumul 14, Numărul 1(15) / 2006 / ISSN 1561-2848 | ||||||
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In this paper we show how the category of re ection quasigroups forms a natural and
suitable context for the development of an abstract theory of the geometric mean, as
it appears in matrix and operator theory. We provide a new characterization of those
quasigroups that arise when re ection quasigroups are endowed with the mean operation.
We also show how the notion of the geometric mean can be enlarged to that of weighted
means, develop basic properties of the latter, and illustrate their usefulness in solving
equations involving the mean operation.
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