On the relationship between the Hausdorff distance and matrix distances of ellipsoids

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 follows 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. © 1983.