Products of Vectors in Max-Plus Algebra
DOI:
https://doi.org/10.58649/2e97gf54Keywords:
Scalar product, vector product, mixed product, orthogonality, an angle between two vectorsAbstract
Idempotent variants of the concepts of scalar, vector, and mixed products of vectors, the angle between two vectors, and the orthogonality of vectors are presented. The differences between these notions in classical analysis and in idempotent analysis are demonstrated, and the properties of these products are also given.
References
G.L. Litvinov, V.P. Maslov, G.B. Ships, Idempotent functional analysis: an algebraic approach, Mathematical Notes, 69(5) (2001), 696–729.
L.D.R. Kocinac, A.A. Zaitov, M.R. Eshimbetov, On the Čech-completeness of the space of τ-smooth idempotent measures. Axioms, 13(8) (2024), 569–582.
M. Eshimbetov, J. Eshimbetov, Y. Abduraimov, On Solution of Systems of Max-Plus Linear Equations, Bulletin of the Institute of Mathematics, 8(2) (2025), 24–35.
J. Gunawardena, Idempotency. Publ. of the Newton Institute, (11) (1998), Cambridge University Press, Cambridge, (Online publication date: May 2010).
K.G. Farlow, Max-Plus Algebra, Blacksburg, Virginia, 91 (2009).
V.N. Kolokolstov, V.P. Maslov, Idempotent Analysis and Its Applications, Springer-Science+Business Media, 401 (1997).
Y. Nishida, S. Watanabe, Y. Watanabe, Independence and orthogonality of algebraic eigenvectors over the max-plus algebra. arXiv:2110.00285v2 [math.CO] (2021).
Downloads
Published
Data Availability Statement
No datasets were generated or analysed during the current study.
Issue
Section
License
Articles published in Journal of Modern Mathematical Studies are distributed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). Authors retain copyright and grant the journal the right of first publication.
