Sifat-Sifat Matriks Normal dalam Aljabar Max-Plus

Authors

  • Any Muanalifah UIN Walisongo Semarang,
  • Yulia Romadiastri UIN Walisongo Semarang, Indonesia
  • Muhammad Ulil Albab UIN Walisongo Semarang, Indonesia
  • Nurwan Universitas Negeri Gorontalo, Indonesia
  • Rosalio G. Artes Mindanao State University - Tawi-Tawi Collage of Technology and Oceanography, Philippines
  • Ainun Esti Candra UIN Walisongo Semarang, Indonesia

Keywords:

aljabar max-plus, matriks normal, matriks komutatif, idempotent

Abstract

Dalam aljabar max-plus, matriks normal didefinisikan sebagai matriks persegi  dimana elemen pada diagonal utamanya adalah nol dan elemen non diagonal utamanya adalah bilangan real non positif. Struktur ini memberikan sifat keteraturan khusus terhadap operasi maksimum dan penjumlahan pada aljabar maxplus. Pada artikel ini akan di bahas review tentang matriks  normal dan perilaku stabil terhadap perpangkatan, termasuk kondisi tertentu yang menjamin sifat idempoten. Selain itu, diperoleh kriteria struktural yang memastikan kekomutatifan dua matriks normal terhadap perkalian max-plus.

Downloads

Download data is not yet available.

References

Baccelli, F., Cohen, G., Olsder, G. J., & Quadrat, J.-P. (1992). Synchronization and Linearity. New York: Wiley.

Bernhard, P. (2000). Max-plus algebra and Mathematical Fear in Dynamic Optimization. Set-Valued Analysis, 8(1), 71-84.

Butkovic, P. (2010). Max Linear Systems: Theory and Algorithms. Springer.

Heidergott, B., Olsder, G. J., & van , J. (2005). Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications. Princeton University Press.

Linde, J., & De La Puente, M. (2015). Matrices Commuting with given Normal Tropical Matrix. Linear Algebra and Its Applications, 482(1), 101-121.

Muanalifah, A., & Sergeev, S. (2020). Modifying the tropical version of Stickel’s key exchange protocol. Applications of Mathematics, 65, 727-753.

Muanalifah, A., & Sergeev, S. (2022). On the tropical discrete logarithm problem and security of a protocol based on tropical semidirect product. Communication in Algebra, 50(2), 861-879.

Nurdin, S. A., Yahya, L., Hasan, I. K., & Nurwan, N. (2023). Model Antrian Pelayanan Terhadap Nasabah Bank BRI Menggunakan Petri Net dan Aljabar Max Plus. Research in the Mathematical and Natural Science, 2(2), 57-63.

Rauf, M. A., Nurwan, N., Yahya, L., & Nuha, A. R. (2021). Model Penjadwalan Proyek Pembangunan Perumahan Menggunakan Petri Net dan Aljabar Max-Plus. Jurnal Edukasi dan Sains Matematika, 7(1).

Sergeev, S. (2009). Max Algebraic Powers of Irreducible Matrices in the Periodic Regime: An Application of Cyclic Classes. Linear Algebra and Its Applications, 431(8), 1325-1339.

Downloads

Published

2025-10-30

Issue

Vol. 7 No. 2 (2025)

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

The Authors submitting a manuscript do so on the understanding that if accepted for publication, copyright of the article shall be assigned to Square: Journal of Mathematics and Mathematics Education as the publisher of the journal. The copyright form should be signed originally and send to the Editorial Office in the form of original mail, scanned document to [email protected] 

Square : Journal of Mathematics and Mathematics Education by Mathematics Department UIN Walisongo Semarang is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.