Approximating real linear operators

Marko Huhtanen, and Olavi Nevanlinna. "Approximating real linear operators." Studia Mathematica 179.1 (2007): 7-25. <http://eudml.org/doc/284572>.

@article{MarkoHuhtanen2007,
abstract = {A framework to extend the singular value decomposition of a matrix to a real linear operator $ℳ : ℂⁿ → ℂ^\{p\}$ 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, ℳ is approximated with a sum of operets.},
author = {Marko Huhtanen, Olavi Nevanlinna},
journal = {Studia Mathematica},
keywords = {real linear matrix analysis; operet; singular value decomposition; matrix nearness problem; approximation number; unitarily invariant norm; Frobenius norms},
language = {eng},
number = {1},
pages = {7-25},
title = {Approximating real linear operators},
url = {http://eudml.org/doc/284572},
volume = {179},
year = {2007},
}

TY - JOUR
AU - Marko Huhtanen
AU - Olavi Nevanlinna
TI - Approximating real linear operators
JO - Studia Mathematica
PY - 2007
VL - 179
IS - 1
SP - 7
EP - 25
AB - A framework to extend the singular value decomposition of a matrix to a real linear operator $ℳ : ℂⁿ → ℂ^{p}$ 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, ℳ is approximated with a sum of operets.
LA - eng
KW - real linear matrix analysis; operet; singular value decomposition; matrix nearness problem; approximation number; unitarily invariant norm; Frobenius norms
UR - http://eudml.org/doc/284572
ER -