NILPOTENTS ZERO DIVISORS OF A MULTIDIMENSIONAL MATRIX

S. Masharipov

doi:10.5281/zenodo.7069796

NILPOTENTS ZERO DIVISORS OF A MULTIDIMENSIONAL MATRIX

12.09.2022 International Scientific Journal "Science and Innovation". Series A. Volume 1 Issue 5

S. Masharipov

Abstract. In this article, the necessary conditions for nilpotency of matrices of three and higher dimensions are studied. In addition, its application to quadratic stochastic operators is presented.

Keywords: nilpotent, quadratic stochastic operators, zero divisor, multidimensional matrix, simplex.

References:

1. Don. D. Vo. 3-dimensional matrix mathematical operations. Dissertation of master’s science, California state University, pp. 60, 2017 2. N. P. Sokolov, Spartial matrices and their applications (Russian), Gosudarstv. Izdat. Fiz. -Mat. Lit., Moscow, 1960, pp,300 MR24-A122. 3. R. Abdulghafor. S. Almotairi. H. Almohamedh. B. Almutairi. A. Bajahzar. S.S. Almutairi. A nonlinear convergence consensus: Extreme doubly stochastic quadratic operators for multi-agent systems. MDPI. Basel. Symmetry. Pp.19. 2020. 4. R.A.Brualdi and J.Csima,“On the plane term rank of a three dimensional matrix,”Proceedings of the American Mathematical Society,vol.54,no.1,pp.471–473,197 5. F.Shahidi, R. Ganikhodzaev and R. Abdulghafor. The dynamics of some extreme doubly stochastic quadratic operators. Middle east journal of scientific research.Malaysia. January 2013. 6. B.C. Arnold. Majorization: here, there and everywhere. Statistical scince. institute of mathematical statistics, Vol.22, No. 3, 2007. 407-413 7. R. Turkmena, E. Vehbi. B. Paksoy , F. Zhang. Some inequalities of majorization type. Linear algebra and its applications 437 (2012) 1305-1316. 8. Majorization, Doubly Stochastic Matrices, and Comparison of Eigenvalues T. Ando Division of Applied Mathematics Research Institute of Applied Electricity Hokkaido University, Sapporo, Japan 9. Constantin P. Niculescu and Lars-Erik Persson convex functions a contemporary approach second expanded edition May 23, 2018. 10. J.W.Moon. Topics on tournament. University of Alberta. 2013 11. U. A. Rozikov. Evolution Operator and Algebras of Sex-linked inheritance. Asia Pacific Mathematics Newslette. Volume 3. Number 1. January 2013 12. R.N.Ganikhodzhaev, F. Mukhammedov. U. A. Rozikov. Quadratic stochastic operators and processes results and open problems. Infinite Dimensional Analysis, Quantum Probability and Related Topics. Vol. 14, No. 2. 20011. 279-335. 13. A.W. Marshall, I. Olkin, B. C. Arnold, Inequalities: Theory of majorization and its application, springer, New York, 2011. 14. R. Kaneiwa, N-dimensional matrices and nth order invariant forms (Japanese). Characterization of arithmetic functions (Proc. Sympos., Res. Inst. Math. Sci., Kyoto University, Kyoto, (1975). Surikaisekiken yusho Kokyuroku 274(1976), 83-97. MR 58-10955.