Explicit general solution to the matrix equation AV 1 BW 5 EVF 1 R

A matrix equation AV+BW = EVF + R is considered, where E, A, B and R are matrices with appropriate dimensions, F is an arbitrarily given Jordan matrix and V and W are the matrices to be determined. A complete explicit general solution for this equation is established based on elementary transformations of polynomial matrices. The proposed solution does not involve the derivative of polynomial matrices and not require the eigenvalues of matrix F to be known. When the eigenvalues of matrix F are prescribed, the solution for matrices V and W can be obtained by carrying out singular value decompositions, thus possesses good numerical stability. An example is employed to illustrate the effect of the proposed approaches.