A framework to extend the singular value decomposition of a matrix to a real linear operator 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, ℳ is approximated with a sum of operets.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-1-2,
author = {Marko Huhtanen and Olavi Nevanlinna},
title = {Approximating real linear operators},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {7-25},
zbl = {1123.15005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-1-2}
}
Marko Huhtanen; Olavi Nevanlinna. Approximating real linear operators. Studia Mathematica, Tome 178 (2007) pp. 7-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-1-2/