The solution to the matrix equation \(AV+BW=EVJ+R\).
The generalized Sylvester matrix equation \(AV+BW=EVJ\) finds application in many problems in linear systems theory. The matrices \(A\), \(E\), \(B\), \(J\), \(V\) and \(W\) are respectively \(n\times n\), \(n\times n\), \(n\times r\), \(p\times p\), \(n\times p\) and \(r\times p\); \(J\) is Jordan and \(V\), \(W\) are to be determined. The author deals with the corresponding inhomogeneous equation \(AV+BW=EVJ+R\) encountered when dealing with complicated linear systems; the matrix \(R\) is \(n\times p\). He obtains the general parametric solution to this equation based on the Smith form reduction of the matrix \([A-sE\;B]\); it is not required the eigenvalues of \(J\) to be known. The proposed solution is illustrated by an example.
scientific article; zbMATH DE number 2140804
scientific article