Explicit solutions to the matrix equation E X F − AX = C
- Author(s): Ai-Guo Wu 1, 2
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Affiliations:
1:
Information and Control Research Center, Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, People's Republic of China;
2: Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, People's Republic of China
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Affiliations:
1:
Information and Control Research Center, Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, People's Republic of China;
- Source:
Volume 7, Issue 12,
15 August 2013,
p.
1589 – 1598
DOI: 10.1049/iet-cta.2013.0075 , Print ISSN 1751-8644, Online ISSN 1751-8652
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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.
Inspec keywords: polynomials; observability; controllability; matrix algebra
Other keywords: characteristic polynomial; generalised Sylvester matrix equations; controllability matrices; observability matrices; matrix pair; real complex matrix representation
Subjects: Algebra; Algebra; Algebra, set theory, and graph theory; Algebra
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