Gregoria Ariyanti, Rosalio Gaid Artes
This paper studies the spectral theory of matrices over the symmetrized max-plus algebra, an extension of classical max-plus algebra that incorporates signed elements and a balance relation. A graph-theoretic interpretation is developed by associating matrices with weighted directed graphs, where the spectral radius is characterized by the maximum cycle mean of the modulus matrix. We establish conditions for the existence of symmetrized. Furthermore, we analyze the relationship between spectral properties and the stability of discrete-event dynamical systems. These results extend the scope of spectral theory and provide a foundation for further developments in applied algebra. © 2026 Pushpa Publishing House, Prayagraj, India.
Widya Mandala Surabaya Catholic University, Indonesia; Tawi-Tawi College of Technology and Oceanography, Mindanao State University, Philippines