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On the solution to the Sylvester matrix equation \(AV+BW=EV\;F\). (English) Zbl 0855.93017

Consider the generalized Sylvester matrix equation \(AV + BW = EVF\), where \(A\), \(B\), \(E\), and \(F\) are known complex matrices of appropriate sizes, and \(V\) and \(W\) are matrices that are to be determined. A complete explicit parametric solution of this equation is provided under the hypotheses that \(F\) is an upper triangular Jordan block, and that the linear descriptor system \(E\dot x = Ax + Bu\) is controllable. The parametrization is given using any pair of right coprime matrix polynomials \(N(s)\) and \(D(s)\) such that \((A - sE)N(s) + BD(s) = 0\).

MSC:

93B25 Algebraic methods
15A24 Matrix equations and identities
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