Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON EIGENVALUES, EIGENVECTORS AND DIAGONAL MATRICES

  • HASAN KELES (Department of Mathematics, Karadeniz Technical University)
  • Received : 2025.05.13
  • Accepted : 2025.12.07
  • Published : 2026.03.30
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Abstract

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 = PDP-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.

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Acknowledgement

The authors sincerely thank the editorial team, journal secretariat, and anonymous reviewers for their careful evaluation and constructive feedback, which greatly improved the clarity and quality of this manuscript.

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