SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesics

Donato Pertici; Alberto Dolcetti

SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesics

Differential Geometry 2022-12-23 v1

Authors: Donato Pertici , Alberto Dolcetti

Abstract

We study the set of generalized principal $\mathfrak{g}$ -logarithms of any matrix belonging to a connected SVD-closed subgroup $G$ of $U_n$ , with Lie algebra $\mathfrak{g}$ . This set is a non-empty disjoint union of a finite number of subsets diffeomorphic to homogeneous spaces, and it is related to a suitable set of minimizing geodesics. Many particular cases for the group $G$ are explicitly analysed.

Keywords

svd-closed subgroups unitary group generalized principal logarithms minimizing geodesics lie algebra homogeneous spaces

Cite

@article{arxiv.2212.11716,
  title  = {SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesics},
  author = {Donato Pertici and Alberto Dolcetti},
  journal= {arXiv preprint arXiv:2212.11716},
  year   = {2022}
}

SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesics

Abstract

Keywords

Cite

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