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.

SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesics / Donato Pertici; Alberto Dolcetti. - STAMPA. - (2022), pp. 1-23.

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

#### 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.
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2022
Donato Pertici; Alberto Dolcetti
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Utilizza questo identificatore per citare o creare un link a questa risorsa: `https://hdl.handle.net/2158/1294619`