Norm inequalities for matrix geometric means of positive definite matrices

DOI10.1080/03081087.2015.1051939zbMath1337.15018OpenAlexW2236071285MaRDI QIDQ2787614

Takeaki Yamazaki, Yuki Seo, Jun Ichi Fujii

Publication date: 4 March 2016

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2015.1051939

zbMATH Keywords

unitarily invariant normKantorovich constantKarcher meanAndo-Hiai inequalitymatrix geometric meanchaotic geometric mean

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45)

Related Items (5)

The quantum ♮α-Rényi divergence of real order ⋮ Log-convexity of generalized Kantorovich function ⋮ Ando–Hiai-type inequalities for operator means and operator perspectives ⋮ Ando–Hiai type inequalities for multivariate operator means ⋮ VARIANTS OF ANDO–HIAI TYPE INEQUALITIES FOR DEFORMED MEANS AND APPLICATIONS

Cites Work

• Norm inequalities related to the matrix geometric mean
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• Monotonic properties of the least squares mean
• Matrix power means and the Karcher mean
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• Geometric means
• Generalized Pólya-Szegő type inequalities for some non-commutative geometric means
• Riemannian metrics on positive definite matrices related to means. II
• Karcher means and Karcher equations of positive definite operators
• The Riemannian mean and matrix inequalities related to the Ando-Hiai inequality and chaotic order
• On the Ando–Li–Mathias mean and the Karcher mean of positive definite matrices
• The Golden-Thompson-Segal type inequalities related to the weighted geometric mean due to Lawson-Lim
• A general framework for extending means to higher orders
• An effective matrix geometric mean satisfying the Ando–Li–Mathias properties
• Inequalities between means of positive operators
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• Geometric Means in a Novel Vector Space Structure on Symmetric Positive‐Definite Matrices
• Norm inequalities for the chaotically geometric mean and its reverse

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