Sylvester’s matrix equation and Roth’s removal rule
FREDERIC HENRY GERRISH, Abigail Ward · The Mathematical Gazette · 1998
In 1952 W. E. Roth published two theorems, one of which has come to be known as Roth’s removal rule and (slightly generalised) goes as follows. [Recall that square matrices M , N are similar when there is an invertible matrix R such that RMR -1 = N . The matrix entries can be elements from any field, although for simplicity we shall call them ‘numbers’.]