Bushell's equations and polar decompositions

DOI10.1002/mana.200610820zbMath1189.47058OpenAlexW1993926453MaRDI QIDQ3647161

Yongdo Lim

Publication date: 30 November 2009

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200610820

zbMATH Keywords

positive definite operatorpolar decompositiongeodesic submanifoldThompson's part metricBushell equation

Mathematics Subject Classification ID

Equations involving nonlinear operators (general) (47J05) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Convex sets and cones of operators (47L07) Operator means involving linear operators, shorted linear operators, etc. (47A64)

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The positive definite solution of the nonlinear matrix equation \(X^p = A + M(B + X^{-1})^{-1} M^\ast\) ⋮ Convex geometric means ⋮ Nonlinear equations based on jointly homogeneous mappings ⋮ On the solution of the nonlinear matrix equation \(X^n=f(X)\) ⋮ A new inversion-free iterative method for solving a class of nonlinear matrix equations

Cites Work

• Means of positive linear operators
• Convexity of the geodesic distance on spaces of positive operators
• On the exponential metric increasing property.
• Finsler metrics on symmetric cones
• Hilbert's metric and positive contraction mappings in a Banach space
• Positive definite matrices
• Metric convexity of symmetric cones
• Application of Hilbert's projective metric on symmetric cones
• Hilbert’s projective metric and iterated nonlinear maps
• The Geometric Mean, Matrices, Metrics, and More
• Geometrical significance of the Löwner-Heinz inequality
• Symmetric spaces with convex metrics
• On Certain Contraction Mappings in a Partially Ordered Vector Space
• Compressions of infinite-dimensional bounded symmetric domains
• Applications of geometric means on symmetric cones

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