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On coprimeness of two polynomials in the framework of conjugate product
Author(s): Ai-Guo Wu, Yuan-Rong Xu
Source: IET Control Theory & Applications, Volume 11, Issue 10, June 2017, p. 1522 - 1529
Type: Article
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The right and left con-Sylvester matrices for two polynomials are defined, and then the criteria for right and left coprimeness of two polynomials in the framework of conjugate product are given in terms of the determinant of the right and left con-Sylvester matrices, respectively. The results in this study can be viewed as a generalisation of the well-known Sylvester resultant criterion for coprimeness of two polynomials in the framework of ordinary product.

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Explicit solutions to the matrix equation E X F − AX = C
Author(s): Ai-Guo Wu
Source:
Type: Article
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The matrix equation E X F − AX = C is investigated in this study, and three approaches are provided to solve this equation. The first approach is to transform it into a real matrix equation with the help of real representation of complex matrices. In the second approach, the solution is given in terms of characteristic polynomial of a constructed matrix pair. In the third approach, the solution can be neatly expressed in terms of controllability matrices and observability matrices. By specialising the obtained solutions of E X F − AX = C, some new expressions of the generalised Sylvester matrix equations are also provided.

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