Solving Linear Matrix Equations by Matrix Decompositions

In this paper, a system of linear matrix equations
is considered. A new necessary and sufficient condition for the
consistency of the equations is derived by means of the generalized
singular-value decomposition, and the explicit representation of the
general solution is provided.

• Yongxin Yuan
• Kezheng Zuo

• Matrix equation
• Generalized inverse
• Generalized singular-value decomposition.

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