Akademik Veri Yönetim Sistemi
ICSAS 6th INTERNATIONAL CONFERENCE ON APPLIED SCIENCES, İzmir, Türkiye, 6 - 08 Şubat 2026, ss.286-305, (Tam Metin Bildiri)
This paper introduces and analyzes Hyper G-pairs, a novel equivalence relation defined on the set of nonsingular n × n matrices. A pair of matrices (A, B) is called a Hyper G-pair if there exist nonsingular diagonal matrices D1 and D2 such that A−T = D1BD2. This relation generalizes classical diagonal equivalence and captures a wider class of structural symmetries in matrices, including non-diagonal and upper triangular forms. We prove that the Hyper G-pair relation is an equivalence relation by establishing its reflexivity, symmetry, and transitivity. Reflexivity is shown for G-matrices, while symmetry and transitivity are verified through explicit construction of the associated diagonal matrices. Several illustrative 4×4 numerical examples, including non-diagonal matrices, are provided to demonstrate the practical computation of A−T = D1BD2 and the verification of equivalence. Moreover, we discuss canonical forms and invariants, such as determinants and selected minors, to characterize equivalence classes. These results contribute to the broader study of matrix equivalence relations, providing new tools for matrix classification and structural analysis in linear algebra and its applications.