Akademik Veri Yönetim Sistemi
21th International Geometry Symposium. In Honor of Prof. Dr. Arif Salimov, Erzurum, Türkiye, 17 - 19 Temmuz 2025, ss.1, (Özet Bildiri)
This work investigates structural transformations and matrix relations within the framework of hybrid numbers, a non-commutative algebraic system unifying complex, dual, and hyperbolic components. We introduce a generalized notion of consimilarity adapted to hybrid matrices, analyze its algebraic properties, and demonstrate its role in classifying equivalence classes. A novel real representation technique is developed to translate hybrid matrix relations into classical forms, enabling the application of real linear algebra tools. Conditions ensuring the existence and uniqueness of solutions to generalized matrix problems are derived using spectral analysis. The study not only broadens the scope of matrix theory to hybrid settings but also offers tools applicable to mathematical physics, control theory, and algebraic systems.