Multi-variable weighted geometric means of positive definite matrices

Title
Multi-variable weighted geometric means of positive definite matrices
Author(s)
이호수Lim, Yongdo[Lim, Yongdo]Yamazaki, Takeaki[Yamazaki, Takeaki]
Keywords
CONVEXITY; SPACES
Issue Date
201107
Publisher
ELSEVIER SCIENCE INC
Citation
LINEAR ALGEBRA AND ITS APPLICATIONS, v.435, no.2, pp.307 - 322
Abstract
We define a family of weighted geometric means {B (t: omega; A)}(t is an element of vertical bar 0.1 vertical bar n) where a) and A vary over all positive probability vectors in R-n and n-tuples of positive definite matrices resp. Each of these weighted geometric means interpolates between the weighted ALM (t = 0(n)) and BMP (t = 1(n)) geometric means CALM and BMP geometric means have been defined by Ando-Li-Mathias and Bini-Meini-Poloni, respectively.)We show that the weighted geometric means satisfy multidimensional versions of all properties that one would expect for a two-variable weighted geometric mean. (C) 2011 Elsevier Inc. All rights reserved.
URI
http://hdl.handle.net/YU.REPOSITORY/24860http://dx.doi.org/10.1016/j.laa.2011.01.026
ISSN
0024-3795
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기초교육대학 > 교양학부 > Articles
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