On n^th Roots of Unity and k^th Order Involutive Matrices
WSEAS TRANSACTIONS ON MATHEMATICS, cilt.25, ss.202-214, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 25
- Basım Tarihi: 2026
- Doi Numarası: 10.37394/23206.2026.25.20
- Dergi Adı: WSEAS TRANSACTIONS ON MATHEMATICS
- Derginin Tarandığı İndeksler: Scopus, INSPEC, zbMATH
- Sayfa Sayıları: ss.202-214
- Karadeniz Teknik Üniversitesi Adresli: Evet
Özet
The n^th roots of unity play a central role in algebra and complex analysis, with important applications in number theory, Fourier analysis, and quantum mechanics. This paper investigates the solutions of the equation x^n = 1 in both real and complex domains, emphasizing their algebraic structureand geometric representation.
We further introduce k^th order involutive matrices as a generalization of classical involutive matrices and analyze their fundamental spectral properties, including eigenvalue distributions and diagonalizability. A direct connection between the n^th roots of unity and the eigenvalues of k^th order involutive matrices is established, providing new insight into their cyclic behavior. These results underscore the relevance of higher-order involutive matrices in linear algebra, quantum mechanics, and computational mathematics.