Approximating real linear operators

Marko Huhtanen¹ ; Olavi Nevanlinna¹

¹ Institute of Mathematics Helsinki University of Technology Box 1100, FIN-02015, Finland

Studia Mathematica, Tome 179 (2007) no. 1, pp. 7-25

Résumé

A framework to extend the singular value decomposition of a matrix to a real linear operator ${\cal M}:{\mathbb C}^n \rightarrow {\mathbb C}^p$ is suggested. To this end real linear operators called operets are introduced, to have an appropriate generalization of rank-one matrices. Then, adopting the interpretation of the singular value decomposition of a matrix as providing its nearest small rank approximations, ${\cal M}$ is approximated with a sum of operets.

Détail

DOI : 10.4064/sm179-1-2

Keywords: framework extend singular value decomposition matrix real linear operator cal mathbb rightarrow mathbb suggested end real linear operators called operets introduced have appropriate generalization rank one matrices adopting interpretation singular value decomposition matrix providing its nearest small rank approximations cal approximated sum operets