MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
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