The Resultant and the Matrix Equation $AX = XB$
Robert E. Hartwig · SIAM Journal on Applied Mathematics · 1972
The concept of a resultant of two polynomials over an arbitrary field is used to reconcile the Cecioni–Frobenius theorem with the theory of direct products, insofar that these are used to establish the existence of a nonzero solution to the matrix equation $AX = XB$.