A. K. Abdikalykov, Kh. D. Ikramov, V. N. Chugunov, “A Duality Relation for Unitary Automorphisms in the Spaces of Toeplitz and Hankel Matrices”, Mat. Zametki, 2016, Volume 99, Issue 1,Pages <nobr>3

A Duality Relation for Unitary Automorphisms in the Spaces of Toeplitz and Hankel Matrices

A. K. Abdikalykov^a, Kh. D. Ikramov^b, V. N. Chugunov^c

^a Kazakhstan Branch of Lomonosov Moscow State University
^b Lomonosov Moscow State University
^c Institute of Numerical Mathematics, Russian Academy of Sciences

Abstract: The duality relation in the title of the paper is an identity between the groups of unitary automorphisms acting in the space of Toeplitz or Hankel matrices by similarity or congruence. A simple answer is given to the question why such identities can emerge.

Keywords: Toeplitz matrix, Hankel matrix, unitary matrix, backward identity matrix, automorphism.

UDC: 519.6

Received: 25.03.2015

DOI: 10.4213/mzm10780