A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity (Q1827477)
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scientific article; zbMATH DE number 2083491
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity |
scientific article; zbMATH DE number 2083491 |
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A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity (English)
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6 August 2004
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Many problems in systems and control theory require the solution of Sylvester's equation \(AX-YB=C\) or of its generalization \((*)\) \(AXB+CYD=E\). The author studies the couple of matrix equations \((**)\) \(A_1XB_1=C_1,A_2XB_2=C_2\) over an arbitrary regular ring with identity. He obtains necessary and sufficient conditions for the consistency of the system \((**)\) and presents its general solution. The results are used to obtain necessary and sufficient conditions for the consistency of the equation \((*)\) and to derive the form of its general solution.
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linear matrix equation
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system of matrix equations
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inner inverse of a matrix
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reflexive inverse of a matrix
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Sylvester matrix equation
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consistency
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regular ring
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0.96491873
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0.9182205
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0.90432274
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0.90395856
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