Abstract
In this paper, a simple method for generating a nonsingular solution of the matrix equation
XH
=
HX where the matrix
H is in unreduced lower Hessenberg form is proposed. The controllability of the matrix pair (
H,
b) where
b is the last column vector of solution matrix
X is also addressed. In addition, a nonsingular symmetric solution of the matrix equation
XH
=
H
T
X is obtained and the matrix pair (
H,
b) where
b is the last row of the solution matrix of this equation is shown to be controllable.