Akademik Veri Yönetim Sistemi
ICSAS 6th INTERNATIONAL CONFERENCE ON APPLIED SCIENCES, İzmir, Türkiye, 6 - 08 Şubat 2026, (Tam Metin Bildiri)
Th s paper ntroduces a new algebra c nterpretat on connect ng Hyper G matr ces w th the class cal Ducc sequence transformat on. By establ sh ng a correspondence between the c rculant structure of r matr ces and terat ve d fference dynam cs, we present a un f ed framework that l nks determ nant-preserv ng matr x pa rs w th cycl c d fference systems. The proposed formulat on reveals how the Hyper G equ valence can be v ewed as a d screte analogue of d fferent al operators act ng on structured matr ces, enabl ng a deeper understand ng of matr x evolut on through success ve Ducc terat ons. Several llustrat ve examples are prov ded to demonstrate the algebra c nvar ants preserved dur ng these transformat ons, such as determ nant constancy and symmetry relat ons w th n the transformat on cha n. Furthermore, a compat b l ty theorem s establ shed to show that Ducc terat ons ma nta n the Hyper G matr x equ valence class under spec f c transformat on constra nts. Th s analyt cal connect on not only contr butes to the theory of mult-valued matr x transformat ons but also opens potent al appl cat ons n computat onal algebra, d screte dynam cal systems, and cod ng theory, where cycl c relat ons and nvar ant preservat on play a central role.