Generalized principal logarithms and Riemannian properties of a class of subgroups of \(\mathbf{U_n}\) endowed with the Frobenius bi-invariant metric

DOI10.1007/s11565-024-00561-1MaRDI QIDQ6657515

Alberto Dolcetti, Donato Pertici

Publication date: 6 January 2025

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

zbMATH Keywords

geodesicsunitary groupsSVD-decompositionFrobenius metricgeneralized principal logarithmSVD-closed subgroups

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) General properties and structure of real Lie groups (22E15) Matrix Lie algebras (15B30)

Cites Work

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• Skew symmetric logarithms and geodesics on \(\mathrm{O}_n(\mathbb{R})\)
• Some remarks on the Jordan-Chevalley decomposition
• Elliptic isometries of the manifold of positive definite real matrices with the trace metric
• Additivity of Jordan multiplicative maps on Jordan operator algebras
• A geometric perspective on the Singular Value Decomposition
• Some additive decompositions of semisimple matrices
• Compact Lie Groups
• Lie Groups and Geometric Aspects of Isometric Actions
• Functions of Matrices
• Real logarithms of semi-simple matrices
• The full group of isometries of some compact Lie groups endowed with a bi-invariant metric

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