The symmetric solutions of the matrix equations AT XA + BT YB = D and AT XA = C, BT XB = D

Huadong Chuanbo Gongye Xueyuan Xuebao/Journal of East China Shipbuilding Institute（2001）

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Abstract

The symmetric solutions of the matrix equations AT XA + BT YB = D and AT XA = C, BT XB = D are considered. Necessary and sufficient conditions for the existence of such solutions and their general forms are derived by using the singular value decomposition and generalized inverses of matrices.

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Key words

Generalized inverses,Matrix equation,Singular value decomposition,Symmetric solution

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