| SOME PROPERTIES OF COMMON HERMITIAN SOLUTIONS OF MATRIX EQUATIONS $A_{1}XA_{1}^{*}=B_{1}$ AND $A_{2}XA_{2}^{*}=B_{2}$ |
| W. Merahi, S. Guedjiba |
Abstract In this paper we provide necessary and sufficient conditions for the pair of matrix equations $ A_{1}XA_{1}^{*}=B_{1} $ and $ A_{2}XA_{2}^{*}=B_{2} $ to have a common hermitian solution in the form $ \frac{X_{1}{+}X_{2}}{2} $, where $ X_{1} $ and $ X_{2} $ are hermitian solutions of the equations $ A_{1}XA_{1}^{*}=B_{1} $ and $ A_{2}XA_{2}^{*}=B_{2}$ respectively.
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Keywords: Moore-Penrose inverse; matrix equation; rank; inertia; hermitian solution; submatrices. |
MSC: 40A05, 40A25, 45G05 |
Pages: 214--229 |
Volume 71 , Issue 3 , 2019 |
