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Closed form solutions to a family of generalized Sylvester matrix equation in form of ∑i=0ϕAiXFi+∑i=0ψBkYFk=∑j=0φEjRFj are given by using the so-called Kronecker matrix polynomials. It is found that the structure of the solutions is independent of the orders ϕ,ψ and φ. This type of uniform closed form solutions includes our early results as special cases. The results provide great convenience to the...
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