An elementary proof of arithmetic-geometric mean inequality of the weighted Riemannian mean of positive definite matrices

DOI10.1016/j.laa.2011.12.006zbMath1260.15035OpenAlexW2002768246WikidataQ115344728 ScholiaQ115344728MaRDI QIDQ1940311

Takeaki Yamazaki

Publication date: 6 March 2013

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

Full work available at URL: https://doi.org/10.1016/j.laa.2011.12.006

zbMATH Keywords

geometric meanmatrix inequalitypositive definite matrixarithmetic-geometric mean inequalitythe Riemannian mean

Mathematics Subject Classification ID

Miscellaneous inequalities involving matrices (15A45)

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Cites Work

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• Monotonicity of the matrix geometric mean
• Monotonic properties of the least squares mean
• Riemannian geometry and matrix geometric means
• A Schwarz inequality for positive linear maps on C\(^*\)-algebras
• Geometric means
• Multi-variable weighted geometric means of positive definite matrices
• Weighted geometric means
• A Schwarz Inequality for Convex Operator Functions
• An effective matrix geometric mean satisfying the Ando–Li–Mathias properties
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices

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