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Heinig's conjectured condition (S) 3 March 2003
 

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)


m-1
j=1
S2

  

Source: Amdeberhan, Tewodros - Department of Mathematics, Tulane University

 

Collections: Mathematics