6 citations · 8 across the 10 of their papers we have counts for
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Some Riemannian properties of endowed with a bi-invariant metric
Donato Pertici, Alberto Dolcetti
We study some properties of endowed with the Frobenius metric , which is, up to a positive constant multiple, the unique bi-invariant Riemannian metric on . In part…
SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesics
Donato Pertici, Alberto Dolcetti
We study the set of generalized principal -logarithms of any matrix belonging to a connected SVD-closed subgroup of , with Lie algebra . This s…
Real logarithms of semi-simple matrices
Donato Pertici
We study the differential structure of the set of real logarithms of a non-singular real matrix, under the assumption that the matrix is either semi-simple or orthogonal.
The full group of isometries of some compact Lie groups endowed with a bi-invariant metric
Alberto Dolcetti, Donato Pertici
We describe the full group of isometries of absolutely simple, compact, connected real Lie groups, of SO(4) and of U(n), endowed with suitable bi-invariant Riemannian metrics.
Real square roots of matrices: differential properties in semi-simple, symmetric and orthogonal cases
Alberto Dolcetti, Donato Pertici
We study the differential and metric structures of the set of real square roots of a non-singular real matrix, under the assumption that the matrix and its square roots are semi-si…
Elliptic isometries of the manifold of definite positive real matrices with the trace metric
Alberto Dolcetti, Donato Pertici
We study the differential-geometric properties of the loci of fixed points of the elliptic isometries of the manifold of definite positive real matrices with the trace metric. We a…
Differential properties of spaces of symmetric real matrices
Alberto Dolcetti, Donato Pertici
We study the differential geometric properties of the manifold of non-singular symmetric real matrices endowed with the trace metric; in case of positive definite matrices we descr…
Skew symmetric logarithms and geodesics on $O_n(\RR)$
Alberto Dolcetti, Donato Pertici
We investigate the connections between the differential-geometric properties of the exponential map from the space of real skew symmetric matrices onto the group of real special or…
Some differential properties of with the trace metric
Alberto Dolcetti, Donato Pertici
In this note we consider some properties of with the Semi-Riemannian structure induced by the trace metric . In particular we study geodesics and curvature te…