On properties of <i>n</i>-parametric and bi-geometric circulant matrices
Enide Andrade, Can Kizilates, Cristina Manzaneda, Hans Nina
article (Uluslararası, Hakemli) | Yazar(lar): Enide Andrade, Can Kizilates, Cristina Manzaneda, Hans Nina | Yıl: 2025 | Dergi/Kurum: COMPUTATIONAL & APPLIED MATHEMATICS | İndeks: WOS.SCI | DOI: 10.1007/s40314-025-03511-5 | Anahtar Kelimeler: <italic>n</italic>-parametric circulant matrix, Bigeometric circulant matrix,
In this paper, we define new classes of circulant matrices, namely, n-parametric and bigeometric circulant matrices. The lower and upper bounds for the spectral norms of particular cases of these matrices are given. Moreover, the spectral decomposition of the n-parametric circulant matrix structure is determined using a Vandermonde matrix, which allows the set of n-parametric circulant matrices to be defined as a noncommutative ring with unity. An expression for the determinants of these matrices is presented. Additionally, we introduce the definition of a bi-geometric circulant matrix, present a closed expression for its Frobenius norm, and provide an upper bound for its spectral norm. Moreover, explicit expressions for the eigenvalues of an n-parametric circulant matrix, whose entries are the Horadam, Fibonacci, Lucas, Jacobsthal, and Pell numbers, are presented.