The entities A, B, X, Y in the title are operators, by which we mean either linear transformations on a finite-dimensional vector space (matrices) or bounded (= continuous) linear transformations on a Banach space. (All scalars will be complex numbers.) The definitions and statements below are valid in both the finite-dimensional and the infinite-dimensional cases, unless the contrary is stated. 1991 Mathematics Subject Classification 15A24, 47A10, 47A62, 47B47, 47B49, 65F15, 65F30.
%0 Journal Article
%1 bhatia1997solve
%A Bhatia, Rajendra
%A Rosenthal, Peter
%D 1997
%J Bulletin of the London Mathematical Society
%K hitting linear_equations sylvesters_equation times
%N 1
%P 1-21
%R 10.1112/S0024609396001828
%T How and Why to Solve the Operator Equation AX−XB = Y
%U http://blms.oxfordjournals.org/content/29/1/1.abstract
%V 29
%X The entities A, B, X, Y in the title are operators, by which we mean either linear transformations on a finite-dimensional vector space (matrices) or bounded (= continuous) linear transformations on a Banach space. (All scalars will be complex numbers.) The definitions and statements below are valid in both the finite-dimensional and the infinite-dimensional cases, unless the contrary is stated. 1991 Mathematics Subject Classification 15A24, 47A10, 47A62, 47B47, 47B49, 65F15, 65F30.
@article{bhatia1997solve,
abstract = {The entities A, B, X, Y in the title are operators, by which we mean either linear transformations on a finite-dimensional vector space (matrices) or bounded (= continuous) linear transformations on a Banach space. (All scalars will be complex numbers.) The definitions and statements below are valid in both the finite-dimensional and the infinite-dimensional cases, unless the contrary is stated. 1991 Mathematics Subject Classification 15A24, 47A10, 47A62, 47B47, 47B49, 65F15, 65F30.},
added-at = {2016-09-08T23:18:42.000+0200},
author = {Bhatia, Rajendra and Rosenthal, Peter},
biburl = {https://www.bibsonomy.org/bibtex/2f6101421a548d57fea528cd15319e1c7/peter.ralph},
doi = {10.1112/S0024609396001828},
eprint = {http://blms.oxfordjournals.org/content/29/1/1.full.pdf+html},
interhash = {812f134a70d64b6a45d6e1206af8e60b},
intrahash = {f6101421a548d57fea528cd15319e1c7},
journal = {Bulletin of the London Mathematical Society},
keywords = {hitting linear_equations sylvesters_equation times},
number = 1,
pages = {1-21},
timestamp = {2016-09-08T23:18:42.000+0200},
title = {How and Why to Solve the Operator Equation {AX−XB = Y}},
url = {http://blms.oxfordjournals.org/content/29/1/1.abstract},
volume = 29,
year = 1997
}