Geometric Mean and Matrix Quadratic Equations

DOI10.1007/16618_2023_48OpenAlexW4377078071MaRDI QIDQ6117605

Mitsuru Uchiyama

Publication date: 19 February 2024

Published in: Matrix and Operator Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/16618_2023_48

zbMATH Keywords

matrix geometric meanmatrix quadratic equation

Mathematics Subject Classification ID

Linear inequalities of matrices (15A39) Linear operator inequalities (47A63) Matrix equations and identities (15A24) Equations involving linear operators, with operator unknowns (47A62) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Cites Work

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• Some results on matrix means
• Functional calculus for sesquilinear forms and the purification map
• Means of positive linear operators
• The Schwarz inequality via operator-valued inner product and the geometric operator mean
• Geometric means
• Symmetric matrix means
• Operator means and matrix quadratic equations
• Series and parallel addition of matrices
• Matrix quadratic equations
• Loewner's Theorem on Monotone Matrix Functions
• Operator functions and the operator harmonic mean

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