Axioms (Jun 2024)
The Existence and Representation of the Solutions to the System of Operator Equations <i>A<sub>i</sub>XB<sub>i</sub></i> + <i>C<sub>i</sub>YD<sub>i</sub></i> + <i>E<sub>i</sub>ZF<sub>i</sub></i> = <i>G<sub>i</sub></i>(<i>i</i> = 1, 2)
Abstract
In this paper, we give the necessary and sufficient conditions for the existence of general solutions, self-adjoint solutions, and positive solutions to the system of AiXBi+CiYDi+EiZFi=Gi(i=1,2) under additional conditions. In addition, we derive the representation of general solutions to the system of AiXBi+CiYDi+EiZFi=Gi(i=1,2), and provide the matrix representation of the self-adjoint solutions and the positive solutions in the sense of the star order.
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