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- Title
COMMON HERMITIAN LEAST-RANK SOLUTION OF MATRIX EQUATIONS A<sub>1</sub>X<sub>1</sub>A<sub>1</sub>* = B<sub>1</sub> AND A<sub>2</sub>X<sub>2</sub>A<sub>2</sub>* = B<sub>2</sub> SUBJECT TO INEQUALITY RESTRICTIONS.
- Authors
Guerarra, Sihem; Guedjiba, Said
- Abstract
In this paper, we establish a set of explicit formulas for calculating the maximal and minimal ranks and inertias of P - X with respect to X, where P ∊ CnH is given, X is a common Hermitian least-rank solution ofmatrix equations A1XA1* = B1 and A2XA2* = B2. As application, we drive necessary and sufficient conditions for X > P (≥ P, < P, ≤ P) in the Löwner partial ordering. As consequence,we give necessary and sufficient conditions for the existence of common Hermitian positive (nonnegative, negative, nonpositive) definite least-rank solution to A1XA2* = B1 and A2XA2* = B2.
- Subjects
HERMITIAN forms; MATRICES (Mathematics)
- Publication
Facta Universitatis, Series: Mathematics & Informatics, 2015, Vol 30, Issue 5, p539
- ISSN
0352-9665
- Publication type
Article