On the relationship between the Hausdorff distance and matrix distances of ellipsoids
Copyright policy )On the relationship between the Hausdorff distance and matrix distances of ellipsoids
AbstractThe 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.
- Stanford University United States
- University of Montreal Canada
- McGill University Canada
- IBM (United States) United States
Numerical Analysis, Algebra and Number Theory, Convex sets without dimension restrictions (aspects of convex geometry), Euclidean analytic geometry, Positive matrices and their generalizations; cones of matrices, matrix distance, Inequalities and extremum problems involving convexity in convex geometry, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Discrete Mathematics and Combinatorics, ellipsoid, Geometry and Topology, Hausdorff distance of subsets of Rn
Numerical Analysis, Algebra and Number Theory, Convex sets without dimension restrictions (aspects of convex geometry), Euclidean analytic geometry, Positive matrices and their generalizations; cones of matrices, matrix distance, Inequalities and extremum problems involving convexity in convex geometry, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Discrete Mathematics and Combinatorics, ellipsoid, Geometry and Topology, Hausdorff distance of subsets of Rn
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