Akademik Veri Yönetim Sistemi
Journal of Applied and Pure Mathematics, cilt.8, ss.1-12, 2026 (Hakemli Dergi)
In this study, we investigate several fundamental properties of
eigenvalues, eigenvectors, and diagonal matrices. The relationships
between the Poloid and other algebraic structures, as well as infinite
products of matrices, are analyzed. The structures and characteristics
of diagonal matrices are examined from a unified perspective. The main
focus of the paper is to represent any regular matrix A in the form A = P
DP −1, where P is a regular matrix and D is a diagonal matrix. Unlike
traditional approaches that primarily compute eigenvalues and
eigenvectors, this work explores these quantities together with the
intrinsic properties of the matrix
P , highlighting their interconnections and algebraic significance.