On eigenvalues of (T+H)-circulants and (T+H)-skew-circulants
A.K. Abdikalykov1, Kh.D. Ikramov2, V.N. Chugunov3
1Lomonosov Moscow State University, Munaitpasova st., 7 Astana, Kazakhstan, 010010
2Lomonosov Moscow State University, Leninskie gory, 1, Moscow, 119991
3Instiute of Numerical Mathematics, Gubkin str., 8, Moscow, Russia, 119991
Keywords: Toeplitz matrix, Hankel matrix, circulant, skew-circulant, eigenvalues
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 Φ ≠ ±1, then the set of matrices that can be represented as sums of a Toeplitz Φ-circulant and a Hankel Φ-circulant is not an algebra.
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