Is every matrix similar to a Toeplitz matrix? Original Research Article

We show that every n×n complex nonderogatory matrix is similar to a unique unit upper Hessenberg Toeplitz matrix. The proof is constructive, and can be adapted to nonderogatory matrices with entries in any field of characteristic zero or characteristic greater than n. We also prove that every n×n complex matrix with nless-than-or-equals, slant4 is similar to a Toeplitz matrix.