A. K. Abdikalykov, Kh. D. Ikramov, V. N. Chugunov, “On eigenvalues of $(T+H)$-circulants and $(T+H)$-skew-circulants”, Sib. Zh. Vychisl. Mat., 2014, Volume 17, Number 2,Pages 111

This article is cited in 2 papers

On eigenvalues of $(T+H)$-circulants and $(T+H)$-skew-circulants

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

^a Lomonosov Moscow State University, Leninskie gory, 1, Moscow, 119991, Russia
^b Kazakhstan Branch of Lomonosov Moscow State University, Munaitpasova st., 7, Astana, 010010, Kazakhstan
^c Instiute of Numerical Mathematics, Gubkin str., 8, Moscow, 119991, Russia

Abstract: Explicit formulas for calculating eigenvalues of the Hankel circulants, Hankel skew-circulants, $(T+H)$-circulants, and $(T+H)$-skew-circulants are obtained. It is shown that if $\phi\ne\pm1$, then the set of matrices that can be represented as sums of a Toeplitz $\phi$-circulant and a Hankel $\phi$-circulant is not an algebra.

Key words: Toeplitz matrix, Hankel matrix, circulant, skew-circulant, eigenvalues.

UDC: 512

Received: 25.03.2013