Groupe d’études et de recherche en analyse des décisions

# On the Relationship Between Hausdorff Distances and Matrix Distances of Ellipsoids

## Jean-Louis Goffin et Alan J. Hoffman

The space of ellipsoids may be metrized by the Hausdorff distance or by the sum of the distance between their centers and a distance between matrices. Various inequalities between metrics are established.

It implies that the square root of positive semidefinite symmetric matrices satisfies a Lipschitz condition, with a constant which depends only on the dimension of the space.

, 15 pages