The conjugate-normal Toeplitz problem

The conjugate-normal Toeplitz problem is the one of characterizing the matrices that are conjugate-normal and Toeplitz at the same time. Based on a result of Gu and Patton and our results related to the normal Hankel problem, we show that a complex matrix is conjugate-normal and Toeplitz if and only if it is in one of the seven classes explicitly described in our paper.