Riv. Mat. Univ. Parma, Vol. 11, No. 2, 2020

Alberto Dolcetti [a] and Donato Pertici [a]

Real square roots of matrices: differential properties in semi-simple, symmetric and orthogonal cases

Pages: 315-333
Received: 20 November 2020
Accepted: 14 December 2020
Mathematics Subject Classification (2010): 15A24, 53C30, 15B10.
Keywords: square root matrix, semi-simple matrix, symmetric matrix, orthogonal matrix, homogeneous space, trace metric, totally geodesic semi-Riemannian submanifold.
Authors address:
[a]: Università di Firenze, Dipartimento di Matematica e Informatica "U. Dini", Firenze, 50134, Italy

This research was partially supported by GNSAGA-INdAM (Italy)

Full Text (PDF)

Abstract: 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.

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