Not every matrix is similar to a Toeplitz matrix

A negative answer to the question “Is every matrix similar to a Toeplitz matrix?” raised by D.S. Mackey, N. Mackey and S. Petrovic [Linear Algebra Appl. 297 (1999) 87] is given. The tool of investigation is a result concerning the structure of the intersection of kernel and range of a Toeplitz matrix, which is of independent interest.