A Hermitian least squares solution of the matrix equation AXB=C subject to inequality restrictions

This paper gives some closed-form formulas for computing the maximal and minimal ranks and inertias of P−X with respect to X, where P∈CHn is given, and X is a Hermitian least squares solution to the matrix equation AXB=C. We derive, as applications, necessary and sufficient conditions for X⩾(⩽,>,...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 64; no. 6; pp. 1752 - 1760
Main Authors Li, Ying, Gao, Yan, Guo, Wenbin
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2012
Subjects
Generalized inverse
Hermitian solution
Inertia
Least squares solution
Matrix equation
Rank
Least squares solution
Rank
Inertia
Hermitian solution
Matrix equation
Generalized inverse
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ISSN0898-1221
1873-7668
DOI10.1016/j.camwa.2012.02.010

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Summary:This paper gives some closed-form formulas for computing the maximal and minimal ranks and inertias of P−X with respect to X, where P∈CHn is given, and X is a Hermitian least squares solution to the matrix equation AXB=C. We derive, as applications, necessary and sufficient conditions for X⩾(⩽,>,<)P in the Löwner partial ordering. In addition, we give necessary and sufficient conditions for the existence of a Hermitian positive (negative, nonpositive, nonnegative) definite least squares solution to AXB=C.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2012.02.010