Inequalities for the Wasserstein mean of positive definite matrices

DOI10.1016/j.laa.2018.03.017zbMath1418.15017arXiv1803.03357OpenAlexW2963141177MaRDI QIDQ2002552

Rajendra Bhatia, Yongdo Lim, Tanvi Jain

Publication date: 12 July 2019

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

Full work available at URL: https://arxiv.org/abs/1803.03357

zbMATH Keywords

positive definite matricesunitarily invariant normmajorisationlog Euclidean meanCartan meanWasserstein mean

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45) Operator means involving linear operators, shorted linear operators, etc. (47A64)

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Cites Work

• Unnamed Item
• Some norm inequalities for matrix means
• A fixed-point approach to barycenters in Wasserstein space
• Norm inequalities related to the matrix geometric mean
• Monotonicity of the matrix geometric mean
• Monotonic properties of the least squares mean
• Wasserstein geometry of Gaussian measures
• Matrix power means and the Karcher mean
• Riemannian geometry and matrix geometric means
• Jensen's inequality for operators and Loewner's theorem
• Means and concave products of positive semi-definite matrices
• Log majorization and complementary Golden-Thompson type inequalities
• On some inequalities for the matrix power and Karcher means
• On a conjecture of Bhatia, Lim and Yamazaki
• Riemannian metrics on positive definite matrices related to means. II
• 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
• Inequalities between means of positive operators
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• On some operator inequalities