Komutatif Matriks ordo 2×2 Atas Aljabar Max-Plus

Authors

  • Any Muanalifah UIN Walisongo Semarang

DOI:

https://doi.org/10.14421/fourier.2023.121.33-40

Keywords:

Aljabar max-plus, komutatif matriks, matriks normal, matriks circulant, generalisasi matriks Kleene star.

Abstract

Pada aljabar klasik, tidak semua matriks saling komutatif, begitu juga di aljabar max-plus. Pada artikel ini kita akan membahas tentang komutatif matriks ordo  atas aljabar max-plus. Selanjutkan kita akan mengkaji matriks komutatif dengan dimensi dalam aljabar maxplus terdiri atas beberapa kelas diantaranya matriks normal, matriks circulant dan generalisasi matriks Kleene star.

Downloads

Download data is not yet available.

References

D. Grigoriev dan V. Shpilrain, “Tropical Cryptography,” Communication in Algebra, vol. 42, no. 6, pp. 2624-2632, 2014.

D. Grigoriev dan V. Shpilrain, “Tropical cryptography II: Extensions by homomorphisms,” Communication in Algebra, vol. 47, no. 10, pp. 4224-4229, 2019.

A. Muanalifah dan S. Sergeev, “On the tropical discrete logarithm problem and security of a protocol based on tropical semidirect product,” Communication in Algebra, vol. 50, no. 2, pp. 861-879, 2022.

S. Kubo dan K. Nishinari, “Applications of max-plus algebra to flow shop scheduling problems,” Discrete Applied Mathematics, vol. 247, pp. 278-293, 2018.

L. Prastiwi dan Y. Listiana, “The Application of Max-Plus Algebra to Determine The Optimal Time of Ikat Kupang Woven Production,” International Journal of Computing Science and Applied Mathematics, vol. 3, no. 2, pp. 77-80, 2017.

R. Cuningham-Green dan P. Butkoviic, “Basis in max-algebra,” Linear Algebra and its Application, vol. 389, pp. 107-120, 2004.

M. Develin, F.Santos dan B. Strumfels, “On the rank of tropical matrix,” arxiv preprint/0312114, 2023.

P. Guillon, Z. Izhakian, M.Mairesse dan G. Merlet, “The ultimate rank of tropical matrices,” Journal of Algebra, vol. 437, pp. 222-248, 2015.

Z. Izhakian dan L. Rowen, “The tropical rank of a tropical matrix,” Communications in Algebra, vol. 37, no. 11, pp. 3912-3927, 2009.

Z. Izhakian, M. Johnson dan M.Kambites, “Tropical Matrix Groups,” Semigroup forum, vol. 96, no. 1, pp. 178-196, 2018.

Z. Izhakian dan S.Margolis, “Semigroup identities in the monoid of two by two tropical matrices,” Semigroup forum, vol. 80, no. 2, 2010.

J. Okninski, “Identities of the semigroup of upper triangular tropical matrices,” Communications in Algebra, vol. 43, no. 10, pp. 4422-4426, 2015.

J. Linde dan M. de la Puente, “Matrices commuting with a given normal tropical matrix,” Linear Algebra and its Applications, pp. 101-121, 2015.

D. Katz, H. Schneider dan S.Sergeev, “On commuting matrices in max-algebra and in classical nonnegative algebra,” Linear Algebra and its Application , vol. 436, no. 2, pp. 276-292, 2012.

R.Morrison dan N. Tran, “The tropical commuting variety,” Linear Algebra and its Applications, vol. 507, pp. 300-321, 2016.

Y. Xie, “On 2 x 2 tropical commuting matrices,” LinearAlgebra and its Applications, vol. 620, pp. 92-108, 2021.

A. Muanalifah dan S. Sergey, “Modifying the Tropical Version of Stickel's Key Exchange Protocol,” Applications of Mathematics, vol. 65, pp. 727-753, 2020.

P. Butkovic, Max-Linear Systems: Thoery and Algorithm, Springer Monographs in Mathematics, Springer-Verlag, 2010.

D. Jones, “Matrix roots in the max-plus algebra,” Linear Algebra and its Application, vol. 631, pp. 10-34, 2021.

R.A.Cuninghame-Green dan P. Butkovic, “The Equation Ax=By over(max,+),” Theoritical Computer Science, vol. 293, pp. 3-12, 2003.

B. Bakhadly, A. Guterman dan M. d. L. Puente, “Normal Tropical (0,-1)-Matrices and Their Orthogonal Sets,” J. Math Sci, vol. 269, pp. 614-631, 2023.

M. Johnson dan M.Kambites, “Multiplicative structure of 2x2 tropical matrices,” Linear Algebra and its Applications, vol. 435, no. 7, pp. 1612-1625, 2011.

Downloads

Published

2023-04-30

How to Cite

Muanalifah, A. (2023). Komutatif Matriks ordo 2×2 Atas Aljabar Max-Plus. Jurnal Fourier, 12(1), 33–40. https://doi.org/10.14421/fourier.2023.121.33-40

Issue

Section

Articles