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Linear Algebra and its Applications
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A new positive definite geometric mean of two positive definite matrices

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1997 English Publisher:Elsevier BVJournal:Linear Algebra and its Applications, volume 251, pages 1-20 (issn: 0024-3795, Copyright policy )
Authors: Vlastimil Pták; Miroslav Fiedler;

doi: 10.1016/0024-3795(95)00540-4

A new positive definite geometric mean of two positive definite matrices

Abstract

The authors introduce a new type of geometric mean of two positive definite (under certain conditions, positive semidefinite) matrices and describe its most important properties. This new concept of a geometric mean is also confronted with the mean introduced by \textit{T. Ando} [Topics on operator inequalities (1978; Zbl 0388.47024)].

Related Organizations
Keywords

geometric mean, Numerical Analysis, Algebra and Number Theory, Miscellaneous inequalities involving matrices, positive definite matrices, Discrete Mathematics and Combinatorics, Geometry and Topology

  • BIP!
    Impact byBIP!
    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 54
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
54
Top 10%
Top 10%
Average
hybrid