A note on the best approximate solution of the equation AXB-C=0

Authors :: Song Chuanning
Xu Qingxiang
Source :: Journal of Shanghai Normal University (Natural Sciences), Vol 47, Iss 1, Pp 22-23 (2018)
Publication Year :: 2018
Publisher :: Academic Journals Center of Shanghai Normal University, 2018.
Abstract: A counterexample is constructed which shows that with respect to the 2-norm,there exist matrices A,B and C such that A† CB† fails to be the best approximate solution of the equation AXB-C=0,where A† and B† are the Moore-Penrose inverses of A and B,respectively.