The symmetric solution of the matrix equations \(AX+YA=C, AXA^ t+BYB^ t=C\), and \((A^ tXA, B^ tXB)=(C,D)\) (Q1208309)
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scientific article; zbMATH DE number 166254
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The symmetric solution of the matrix equations \(AX+YA=C, AXA^ t+BYB^ t=C\), and \((A^ tXA, B^ tXB)=(C,D)\) |
scientific article; zbMATH DE number 166254 |
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The symmetric solution of the matrix equations \(AX+YA=C, AXA^ t+BYB^ t=C\), and \((A^ tXA, B^ tXB)=(C,D)\) (English)
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16 May 1993
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The authors derive necessary and sufficient conditions for the existence of and the expressions for the symmetric solutions of the matrix equations (I) \(AX+YA=C\), (II) \(AXA^ T+BYB^ T=C\) and (III) \((A^ TXA,B^ TXB)=(C,D)\). In addition, the minimum-2-norm least-squares symmetric solution of equation (I), the minimum-2-norm symmetric solution of equation (II) and the least-squares solution of equation (III) are obtained.
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matrix equations
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minimum-2-norm least-squares symmetric solution
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