Homogeneous linear matrix equation AX =XB and inhomogeneous linear matrix equation AX-XB=C were very important in matrix theory.Two classes matrix equations were solved by elementa-ry method and the explicit solutions were given.%齐次线性矩阵方程AX=XB和非齐次线性矩阵方程AX-XB=C是矩阵论中的重要问题,用初等方法解决了这两类问题并给出解的表达式.
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