On the Ando–Li–Mathias mean and the Karcher mean of positive definite matrices

DOI10.1080/03081087.2014.896359zbMath1322.47019OpenAlexW2084047272MaRDI QIDQ2938366

Jun Ichi Fujii, Yuki Seo

Publication date: 14 January 2015

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

Full work available at URL: https://doi.org/10.1080/03081087.2014.896359

zbMATH Keywords

unitarily invariant normKantorovich constantKarcher meanAndo-Hiai inequalitymatrix geometric meanAndo-Li-Mathias geometric meanSpecht ratiochaotic geometric mean

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Linear operator inequalities (47A63) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (7)

On the Lawson-Lim means and Karcher mean for positive invertible operators ⋮ The upper boundary for the ratio between n-variable operator power means ⋮ Matrix power means and the information monotonicity ⋮ Norm inequalities for matrix geometric means of positive definite matrices ⋮ Ando–Hiai-type inequalities for operator means and operator perspectives ⋮ Generalized versions of reverse Young inequalities ⋮ Determinant for positive operators and operator geometric means

Cites Work

• Norm inequalities related to the matrix geometric mean
• Monotonicity of the matrix geometric mean
• Matrix power means and the Karcher mean
• Zur Theorie der elementaren Mittel
• Riemannian geometry and matrix geometric means
• Log majorization and complementary Golden-Thompson type inequalities
• Geometric means
• Generalized Pólya-Szegő type inequalities for some non-commutative geometric means
• Riemannian metrics on positive definite matrices related to means. II
• A reverse inequality for the weighted geometric mean due to Lawson--Lim
• Karcher means and Karcher equations of positive definite operators
• Riemannian Distances between Geometric Means
• The Riemannian mean and matrix inequalities related to the Ando-Hiai inequality and chaotic order
• 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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