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A LINK BETWEEN COMPLEX NUMBERS IN SYMMETRIZED MAX-PLUS ALGEBRA AND CONVENTIONAL ALGEBRA
Keywords:
complex, conventional, max-plus, link, symmetrizedDOI:
https://doi.org/10.17654/0972087126007Abstract
In this paper, we discuss a link between complex numbers over symmetrized max-plus algebra and conventional complex numbers. The discussion was done by extending a link between symmetrized max-plus algebra and conventional algebra. The result is the corresponding function which is a link between complex numbers over symmetrized max-plus algebra and conventional complex numbers. Also, the corresponding addition and multiplication problems in complex numbers over symmetrized max-plus algebra into conventional complex numbers, and vice versa have been discussed.
Received: April 21, 2025
Revised: June 24, 2025
Accepted: August 12, 2025
References
[1] J. B. Reade, Calculus with Complex Numbers, Taylor & Francis, London, 2003.
[2] J. Kortemeyer, Complex Numbers: An Introduction to First Year Students, Springer, 2021.
[3] M. Akian, R. Bapat and S. Gaubert, Max-plus Algebra: Handbook of Linear Algebra, Chapman and Hall, 2007.
[4] B. Heidergot, G. J. Olsder and J. Woude, Max Plus at Work, Princeton University Press, New Jersey, 2006.
[5] F. Baccelli, G. Cohen, G. L. Olsder and J. P. Quadrat, Synchronization and Linearity, Wiley, New York, 2001.
[6] B. De Schutter, Max-algebraic System Theory for Discrete Event Systems, Ph. D. Dissertation, Departement of Electrical Engineering Katholieke Universiteit Leuven, Leuven, 1996.
[7] B. De Schutter and B. De Moor, The QR decomposition and the singular value decomposition in the symmetrized max-plus algebra, SIAM Journal on Matrix Analysis and Applications 19(2) (1998), 378-406.
[8] B. De Schutter and B. De Moor, The QR decomposition and the singular value decomposition in the symmetrized max-plus algebra revisited, SIAM Journal on Matrix Analysis and Applications 44(3) (2002), 417-454.
[9] Suroto, A. Suparwanto and D. J. E. Palupi, The LU-decomposition in the symmetrized max-plus algebra, Far East Journal of Mathematical Sciences (FJMS) 108(2) (2018), 253-272.
[10] Suroto, A. Suparwanto and D. J. E. Palupi, The Cholesky decomposition of matrices over the symmetrized max-plus algebra, IAENG International Journal of Applied Mathematics 52(3) (2022), 678-683.
[11] Suroto, A. Suparwanto and D. J. E. Palupi, Characterization of rank of a matrix over the symmetrized max-plus algebra, Jordan Journal of Mathematics and Statistics (JJMS) 15(4A) (2022), 843-856.
[12] Suroto, The Moore-Penrose inverse in the symmetrized max-plus algebraic matrix using singular value decomposition, Palestine Journal of Mathematics 13(4) (2024), 135-143.
[13] S. Suroto, N. Istikaanah and R. Renny, The Existence of the Moore-Penrose Inverse in Symmetrized Max-plus Algebraic Matrix, Advances in Physics Research Soedirman International Conference on Mathematics and Applied Sciences (SICOMAS 2021), Vol. 5, 2022, pp. 59-64.
[14] S. Suroto, A. Wardayani and N. Istikaanah, The Weak Substitution in Complex Numbers over the Symmetrized Max-plus Algebra, Proceeding ICMASURE, 2025, pp. 161-167.
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