Skew symmetric logarithms and geodesics on \(\mathrm{O}_n(\mathbb{R})\)

DOI10.1515/advgeom-2018-0012zbMath1404.53052arXiv1611.00588OpenAlexW2963701421MaRDI QIDQ1629390

Donato Pertici, Alberto Dolcetti

Publication date: 11 December 2018

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.00588

zbMATH Keywords

Riemannian manifoldsexponential mapdiameterPfaffiangeodesic curvespairs of (weakly) diametral orthogonal matricessingular value decomposition of skew symmetric matricesskew symmetric and orthogonal matricesskew symmetric and principal logarithmstrace and Frobenius metrics

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Matrix exponential and similar functions of matrices (15A16)

Related Items (5)

The orthogonal Lie algebra of operators: ideals and derivations ⋮ Real logarithms of semi-simple matrices ⋮ A new method to interpolate POD reduced bases–Application to the parametric model order reduction of a gas bearings supported rotor ⋮ The full group of isometries of some compact Lie groups endowed with a bi-invariant metric ⋮ Elliptic isometries of the manifold of positive definite real matrices with the trace metric

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