Roth's similarity theorem and rank minimization in the presence of nonderogatory or semisimple eigenvalues
Augusto Ferrante, Hȧrald K. Wimmer · Linear and Multilinear Algebra · 2012
Roth's similarity theorem on the consistency of Sylvester's matrix equation AX − XA = C can be extended to a theorem on rank minimization if the common eigenvalues of A and B are nonderogatory or semisimple.