On additive decompositions of solutions of the matrix equation \(AXB=C\)
The author considers the triple of matrix equations \(AXB=C\) and \(A_iX_iB_i=C_i\), \(i=1,2\). He studies the possible presentation (when the consistency conditions are met) of the solution \(X\) to the first one as a sum of the solutions \(X_i\) to the last two of them. Applications are given on additive decompositions of generalized inverses and of decompositions of matrix equations into sums of solutions to their small equations.
scientific article; zbMATH DE number 5822855