Akademik Veri Yönetim Sistemi
TROIA 3RD INTERNATIONAL CONFERENCE ON APPLIED SCIENCES, Çanakkale, Türkiye, 27 - 28 Şubat 2026, ss.30-40, (Tam Metin Bildiri)
This study provides a comprehensive and systematic investigation of Q-circulant matrices, focusing on their algebraic, spectral, and operatorial properties, while highlighting their intrinsic connections to Hyper G-matrix pairs. Q-circulant matrices, as a natural generalization of classical circulant structures through the introduction of a deformation parameter Q, exhibit rich mathematical behaviors that extend beyond traditional cyclic matrices. One of the key findings of this work is that these matrices demonstrate scale-symmetry under inverse-transpose operations, which establishes that the pairs (CQ, CQ −1) naturally form Hyper G-matrix pairs. This structural property is further elucidated through the Q-Fourier transform, which diagonalizes Q-circulant matrices and reveals a tight correspondence between the spectra of a matrix and its inverse under scaling. In addition, the study explores the role of anti-automorphisms, specifically the ϕ map, which preserves the Hyper G structure and induces well-defined spectral relations, highlighting both algebraic and operatorial symmetries. Beyond theoretical insights, the paper discusses practical applications, including q-Fourierbased convolutions in signal processing, q-deformed unitary operators in quantum information, modular cyclic structures for cryptography, and spectral factorization techniques in matrix analysis. Overall, this work provides a unifying framework for understanding Q-circulant matrices as a q-deformed subclass of Hyper G structures, offering both fundamental theoretical results and potential avenues for applied research in computational and physical systems.