On solutions of matrix equation XF − AX = C and XF − A X = C over quaternion field
On solutions of matrix equation XF − AX = C and XF − A X = C over quaternion field
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发表时间：
2011
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通讯作者：
Caiqin Song;Guoliang Chen
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文献类型：
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作者：
Caiqin Song;Guoliang Chen
利用克罗内克图和四元数矩阵的复表示，建立了四元数矩阵方程XF−AX=C和XF−A�X=C的显式解。其中一种解可以用对称矩阵、可控性矩阵和可观性矩阵简洁地表达。此外，还给出了这两个方程的两种实用算法。
By means of Kronecker map and complex representation of a quaternion matrix, some explicit solutions to the quaternion matrix equations XF − AX = C and XF − A� X = C are established. One of the solutions is neatly expressed by a symmetric matrix, a controllability matrix and an observability matrix. In addition, two practical algorithms for these two equations are given.