 
Summary: Heinig's conjectured condition (S)
3 March 2003
Abstract
1 Introduction
Mackey, Mackey and Petrovic [2] posed the question "Are all matrices similar
to a Toeplitz matrix?" They showed that every n × n complex nonderogatory
matrix is similar to a unique upper Hessenberg Toeplitz matrix, and also that
every lower dimensional (n 4) complex matrix is similar to a Toeplitz matrix.
The general case is treated in an important paper [1] where Heinig gave the
answer in the negative. Among the many results spread about the latter article,
we have
Theorem 6.1. Assume m 4 is such that condition (S) is fulfilled. Then the
class M (2m, m, m  1) is empty. That means there is no Toeplitz matrix that
is similar to
(1)
m1
j=1
S2
