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

Donato Pertici, Alberto Dolcetti

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 s…