Structure preserving matrix means on the Marcus-Minc stochastic matrices

Title
Structure preserving matrix means on the Marcus-Minc stochastic matrices
Author(s)
이호수Lim, Yongdo[Lim, Yongdo]
Keywords
GEOMETRIC MEANS; TRANSITION MATRICES
Issue Date
201211
Publisher
ELSEVIER SCIENCE INC
Citation
LINEAR ALGEBRA AND ITS APPLICATIONS, v.437, no.10, pp.2397 - 2407
Abstract
In this paper we show that the set PSm of all m x m positive definite stochastic matrices with diagonal entries bounded above by 1/m-1 is stable under the weighted geometric mean operation. It is further shown that PSm is stable for some well-known multivariable matrix means; the least squares means for the Riemannian trace metric and the Kullback-Leibler divergence on the convex cone of m x m positive definite matrices, and ALM (Ando-Li-Mathias) and BMP (Bini-Meini-Poloni) geometric means. (C) 2012 Elsevier Inc. All rights reserved.
URI
http://hdl.handle.net/YU.REPOSITORY/26940http://dx.doi.org/10.1016/j.laa.2012.06.023
ISSN
0024-3795
Appears in Collections:
기초교육대학 > 교양학부 > Articles
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