Title : ( Solvability of the matrix inequality AXA^*+BX^*B^*\geq C )
Authors: mehdi vosough , Mohammad Sal Moslehian ,
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Abstract
In this paper, we first investigate the matrix equation $ AXB+CYD=G $, where $ A, B, C, D $ and $ G $ are arbitrary matrices in a new fashion. Then, we establish some necessary and sufficient conditions for the existence of a solution of $ AXA^*+BX^*B^*\geq C $, where $ A, B $ are arbitrary matrices and $C $ is a Hermitian matrix. In the special case when $ B=A $, we determine the general solution of $ A(X+X^*)A^*\geq C $, where $A $ is an arbitrary matrix and $ C $ is a Hermitian matrix.
Keywords
Matrix equation; matrix inequality; L\"{o}wner partial ordering; generalized inverse
@article{paperid:1069306,
author = {Vosough, Mehdi and Sal Moslehian, Mohammad},
title = {Solvability of the matrix inequality AXA^*+BX^*B^*\geq C},
journal = {Linear and Multilinear Algebra},
year = {2018},
volume = {66},
number = {9},
month = {October},
issn = {0308-1087},
pages = {1799--1818},
numpages = {19},
keywords = {Matrix equation; matrix inequality; L\"{o}wner partial ordering; generalized inverse},
}
%0 Journal Article
%T Solvability of the matrix inequality AXA^*+BX^*B^*\geq C
%A Vosough, Mehdi
%A Sal Moslehian, Mohammad
%J Linear and Multilinear Algebra
%@ 0308-1087
%D 2018
