Approximating real linear operators
Volume 179 / 2007
Studia Mathematica 179 (2007), 7-25
MSC: 15A18, 15A04.
DOI: 10.4064/sm179-1-2
Abstract
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.
