2025/10/19 by Wilson Arley Martinez, Martinez, Wilson Arley, Samin Ingrid Ceron +1
Physics and Astronomy · Computer Science · Mathematics · #Advanced Mathematical Theories and Applications #Matrix Theory and Algorithms #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2510.16934
In this paper, we construct Pell matrices, analogous to Fibonacci matrices, to study algebraic properties of Pell numbers via linear algebra. This framework yields identities involving the trace, inverse, and determinant, as well as matrix products that generate recurrence relations and closed-form expressions. Additionally, we classify all binary 3x3 matrices that generate the Pell equation through conjugation, providing a complete characterization of such matrices.