Monotonic properties of the least squares mean
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Publication:641850
DOI10.1007/s00208-010-0603-6zbMath1229.15024arXiv1007.4792OpenAlexW1984360776MaRDI QIDQ641850
Publication date: 25 October 2011
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1007.4792
positive definite matricesgeometric meanweighted least squarestrace metricLoewner orderingleast squares mean
Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45) Means (26E60) Operator means involving linear operators, shorted linear operators, etc. (47A64)
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Cites Work
- Monotonic properties of the least squares mean
- Noncommutative geometric means
- Riemannian geometry and matrix geometric means
- Riemannian geometry for the statistical analysis of diffusion tensor data
- Geometric means
- Über monotone Matrixfunktionen
- An extended Lie--Trotter formula and its applications
- A Riemannian framework for tensor computing
- Beiträge zur Störungstheorie der Spektralzerlegung
- Weighted geometric means
- A general framework for extending means to higher orders
- An effective matrix geometric mean satisfying the Ando–Li–Mathias properties
- Riemannian center of mass and mollifier smoothing
- Upper and lower bounds for the arithmetic-geometric-harmonic means of positive definite matrices
- The Geometric Mean, Matrices, Metrics, and More
- A Panoramic View of Riemannian Geometry
- A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
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