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Siberian Journal of Numerical Mathematics

2017 year, number 4

A description of pairs of the quasi-commuting Toeplitz and Hankel matrices

V.N. Chugunov1, Kh.D. Ikramov2
1Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina st., 8, Moscow, Russia, 119333
2Lomonosov Moscow State University, Moscow, Leninskie Gory, Russia, 119991
Keywords: теплицева матрица, ганкелева матрица, П•-циркулянт, квазикоммутирующие матрицы, Toeplitz matrix, Hankel matrix, П•-circulant, quasi-commuting matrices

Abstract

We say that the square matrices A and B are of the same order quasi-commute if AB = σ BA for some scalar σ. Classical relations of commutation and anti-commutation are particular cases of this definition. We give a complete description of pairs of the quasi-commuting Toeplitz and Hankel matrices for σ ≠ ± 1.