Geodesic
Similarity automorphisms of the space of Hankel matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 5-12

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The paper describes the nonsingular matrices $U$ such that for every Hankel matrix $A$ of the same order, $U^{-1}AU$ also is a Hankel matrix. 
@article{ZNSL_2019_482_a0,
     author = {A. K. Abdikalykov and Kh. D. Ikramov},
     title = {Similarity automorphisms of the space of {Hankel} matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--12},
     publisher = {mathdoc},
     volume = {482},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a0/}
}
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A. K. Abdikalykov; Kh. D. Ikramov. Similarity automorphisms of the space of Hankel matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 5-12. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a0/