Zobrazeno 1 - 10
of 37
pro vyhledávání: '"Dolcetti, Alberto"'
Autor:
Pertici, Donato, Dolcetti, Alberto
We study some properties of $SU_n$ endowed with the Frobenius metric $\phi$, which is, up to a positive constant multiple, the unique bi-invariant Riemannian metric on $SU_n$. In particular we express the distance between $P, Q \in SU_n$ in terms of
Externí odkaz:
http://arxiv.org/abs/2402.12209
SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesics
Autor:
Pertici, Donato, Dolcetti, Alberto
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 diffeom
Externí odkaz:
http://arxiv.org/abs/2212.11716
Autor:
Dolcetti, Alberto, Pertici, Donato
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.
Externí odkaz:
http://arxiv.org/abs/2106.06413
Autor:
Dolcetti, Alberto, Pertici, Donato
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-simple, or symmetric, or orthogonal.
Externí odkaz:
http://arxiv.org/abs/2010.15609
Autor:
Dolcetti, Alberto, Pertici, Donato
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 also give an explicit description of such loci and in particular we fin
Externí odkaz:
http://arxiv.org/abs/2001.10250
Akademický článek
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Autor:
Dolcetti, Alberto, Pertici, Donato
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 describe the full group of isometries
Comment: 17 pages
Comment: 17 pages
Externí odkaz:
http://arxiv.org/abs/1807.01113
Autor:
Dolcetti, Alberto, Pertici, Donato
Under suitable hypotheses on the ground field and on the matrix $M$, we discuss existence, uniqueness and properties of some additive decompositions of $M$ and of its image through a convergent series.
Externí odkaz:
http://arxiv.org/abs/1707.09239
Autor:
Dolcetti, Alberto, Pertici, Donato
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we obtain some f
Externí odkaz:
http://arxiv.org/abs/1707.01794
Autor:
Dolcetti, Alberto, Pertici, Donato
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 orthogonal matrices and the manifold of real orthogonal matrices equippe
Externí odkaz:
http://arxiv.org/abs/1611.00588