Nonhomogeneous Karcher equations with vector fields on positive definite matrices

DOI10.1007/s40879-021-00469-6zbMath1492.58003OpenAlexW3167281016MaRDI QIDQ2049072

Fumio Hiai, Yongdo Lim, Jimmie D. Lawson

Publication date: 24 August 2021

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40879-021-00469-6

zbMATH Keywords

positive definite matrixRiemannian trace metricgeodesically convex functiongradient equationKarcher mean and equationLambert \(W\) operator function and equationuniform convex function

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Convexity of real functions of several variables, generalizations (26B25) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (2)

Non-homogeneous Riemannian gradient equations for sum of squares of Bures-Wasserstein metric ⋮ Constraint qualifications and optimality criteria for nonsmooth multiobjective programming problems on Hadamard manifolds

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