location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword distance function

 Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2004 (vol 56 pp. 776)

Lim, Yongdo
 Best Approximation in Riemannian Geodesic Submanifolds of Positive Definite Matrices We explicitly describe the best approximation in geodesic submanifolds of positive definite matrices obtained from involutive congruence transformations on the Cartan-Hadamard manifold ${\mathrm{Sym}}(n,{\Bbb R})^{++}$ of positive definite matrices. An explicit calculation for the minimal distance function from the geodesic submanifold ${\mathrm{Sym}}(p,{\mathbb R})^{++}\times {\mathrm{Sym}}(q,{\mathbb R})^{++}$ block diagonally embedded in ${\mathrm{Sym}}(n,{\mathbb R})^{++}$ is given in terms of metric and spectral geometric means, Cayley transform, and Schur complements of positive definite matrices when $p\leq 2$ or $q\leq 2.$ Keywords:Matrix approximation, positive, definite matrix, geodesic submanifold, Cartan-Hadamard manifold,, best approximation, minimal distance function, global tubular, neighborhood theorem, Schur complement, metric and spectral, geometric mean, Cayley transformCategories:15A48, 49R50, 15A18, 53C3
 top of page | contact us | privacy | site map |