On the matrix equations $AX - XB = C$ and $AX - YB = C$
Harley Flanders, Hȧrald K. Wimmer · SIAM Journal on Applied Mathematics · 1977
W. E. Roth gave necessary and sufficient conditions for the solvability of each of the matrix equations $AX - XB = C$ and $AX - YB = C$. His proofs were based on canonical forms. In this note we give invariant proofs of Roth’s theorems.