Table of Contents
Conference Papers in Mathematics
Volume 2013, Article ID 425608, 7 pages
Conference Paper

Approximating Sets of Symmetric and Positive-Definite Matrices by Geodesics

1Institute of Systems and Robotics, University of Coimbra, Pólo II, Pinhal de Marrocos, 3030-290 Coimbra, Portugal
2Department of Mathematics, University of Trás-os-Montes and Alto Douro, Apartado 1013, 5001-801 Vila Real, Portugal
3Department of Mathematics, University of Coimbra, Largo D. Dinis, 3001-454 Coimbra, Portugal

Received 14 June 2013; Accepted 10 July 2013

Academic Editors: G. S. F. Frederico, N. Martins, D. F. M. Torres, and A. J. Zaslavski

This Conference Paper is based on a presentation given by L. Machado at “The Cape Verde International Days on Mathematics 2013” held from 22 April 2013 to 25 April 2013 in Praia, Cape Verde.

Copyright © 2013 L. Machado and F. Silva Leite. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We formulate a generalized version of the classical linear regression problem on Riemannian manifolds and derive the counterpart to the normal equations for the manifold of symmetric and positive definite matrices, equipped with the only metric that is invariant under the natural action of the general linear group.