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

Authors

W. Merahi Departement of Mathematics, Faculty of Sciences, University of Batna 2, Batna, Algeria Author
S. Guedjiba Departement of Mathematics, Faculty of Sciences, University of Batna 2, Batna, Algeria Author

Keywords:

Moore-Penrose inverse, matrix equation, rank, inertia, hermitian solution, submatrices

Subjects:

40A05, 40A25, 45G05

Abstract

In this paper we provide necessary and sufficient conditions for the pair of matrix equations $A_{1} X A_{1}^{*} = B_{1}$ and $A_{2} X A_{2}^{*} = B_{2}$ 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 $A_{1} X A_{1}^{*} = B_{1}$ and $A_{2} X A_{2}^{*} = B_{2}$ respectively.

SOME PROPERTIES OF COMMON HERMITIAN SOLUTIONS OF MATRIX EQUATIONS $A_{1} X A_{1}^{} = B_{1}$ AND $A_{2} X A_{2}^{} = B_{2}$

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SOME PROPERTIES OF COMMON HERMITIAN SOLUTIONS OF MATRIX EQUATIONS A1XA1∗=B1 AND A2XA2∗=B2

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SOME PROPERTIES OF COMMON HERMITIAN SOLUTIONS OF MATRIX EQUATIONS $A_{1} X A_{1}^{} = B_{1}$ AND $A_{2} X A_{2}^{} = B_{2}$