Geometric properties of positive definite matrices cone with respect to the Thompson metric
type: Item
instance of: scholarly article
title: Geometric properties of positive definite matrices cone with respect to the Thompson metric
zbMATH Open document ID: 1221.15045
author: Masatoshi Ito
author: Yuki Seo
author: Takeaki Yamazaki
author: Masahiro Yanagida
published in: Linear Algebra and its Applications
publication date: 2011-07-15T00:00:00Z
review text: The \textit{generalized geometric mean} of two positive definite matrices \(A\) and \(B\) is defined to be \(A \sharp_s B:= A^{\frac 12} \big( A^{-\frac 12}BA^{-\frac 12} \big)^s A^{\frac 12}\). \(A\sharp B:= A\sharp_{\frac 12} B\) is the well-known geometric mean. The authors discuss geometric properties of a quadrangle with parallelogramic properties in a convex cone of positive definite matrices with respect to the Thompson metric as introduced by \textit{A. C. Thompson} [Proc. Am. Math. Soc. 14, 438--443 (1963; Zbl 0147.34903)].
reviewed by: Igor Klep
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 47A64
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 5924570
zbMATH Keywords: positive definite matrix
zbMATH Keywords: Thompson metric
zbMATH Keywords: geometric mean
MaRDI profile type: Publication
full work available at URL: j.laa.2011.03.063
OpenAlex ID: W2006189886
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DOI: 10.1016/J.LAA.2011.03.063
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description: scientific article; zbMATH DE number 5924570