آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 447 |
| تعداد مقالات | 4,557 |
| تعداد مشاهده مقاله | 5,380,003 |
| تعداد دریافت فایل اصل مقاله | 3,580,071 |
Two-sided sgut-majorization and its linear preservers | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 339-347 اصل مقاله (491.9 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19692.1277 | ||
| نویسنده | ||
| Asma Ilkhanizadeh Manesh* | ||
| Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box: 7713936417, Rafsanjan, Iran | ||
| چکیده | ||
| Let $\textbf{M}_{n,m}$ be the set of all $n$-by-$m$ real matrices, and let $\mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. An $n$-by-$m$ matrix $R=[r_{ij}]$ is called g-row substochastic if $\sum_{k=1}^{m} r_{ik}\leq 1$ for all $i\ (1\leq i \leq n)$. For $x$, $y \in \mathbb{R}^{n}$, it is said that $x$ is $\textit{sgut-majorized}$ by $y$, and we write $ x \prec_{sgut}y$ if there exists an $n$-by-$n$ upper triangular g-row substochastic matrix $R$ such that $x=Ry$. Define the relation $\sim_{sgut}$ as follows. $x\sim_{sgut}y$ if and only if $x$ is sgut-majorized by $y$ and $y$ is sgut-majorized by $x$. This paper characterizes all (strong) linear preservers of $\sim_{sgut}$ on $\mathbb{R}^{n}$. | ||
| کلیدواژه‌ها | ||
| Generalized row substochastic matrix؛ (strong) linear pre- server؛ two-sided sgut-majorization | ||
| مراجع | ||
|
[1] T. Ando, Majorization, doubly stochastic matrices, and comparision of eigenvalues, Linear Algebra Appl., 118 (1989), pp. 163-248.
[2] T. Ando, Majorization and inequalities in matrix theory, Linear Algebra Appl., 199 (1994), pp. 17-67.
[3] A. Armandnejad and Z. Gashool, Strong linear preservers of g-tridiagonal majorization on Rn, Electronic. J. Linear Algebra, 23 (2012), pp. 115-121.
[4] A. Armandnejad and A. Ilkhanizadeh Manesh, Gut-majorization and its linear preservers, Electronic. J. Linear Algebra, 23 (2012), pp. 646-654.
[5] H. Chiang and C. K. Li, Generalized doubly stochastic matrices and linear preservers, Linear and Multilinear Algebra, 53 (2005), pp. 1-11.
[6] G.H. Hardy, J.E. Littlewood, and G. Polya, Some simple inequalities satisfed by convex functions., Messenger of Mathematics , 58 (1929), pp. 145-152.
[7] A. M. Hasani and M. Radjabalipour, The structure of linear operators strongly preserving majorizations of matrices, Electron. J. Linear Algebra, 15 (2006), pp. 260-268.
[8] A. M. Hasani and M. Radjabalipour, On linear preservers of (right) matrix majorization, Linear Algebra Appl, 423 (2007), pp. 255-261.
[9] A. Ilkhanizadeh Manesh, On linear preservers of sgut-majorization on Mn;m, Bull. Iranian Math. Soc., 42 (2016), pp. 470-481.
[10] A. Ilkhanizadeh Manesh, Right gut-Majorization onMn;m, Electron. J. Linear Algebra, 31 (2016), pp. 13-26.
[11] A. W. Marshall, I. Olkin, and B. C. Arnold, Inequalities: Theory of majorization and its applications, Springer, New York, 2011.
[12] I. Schur, Uber enie klasse von mittelbildungen mit anwendungen auf die determinan-tentheorie, Sitzungsberichte der Berliner Mathematischen Gesellschaft, 22 (1923), pp.9-20. | ||
|
آمار تعداد مشاهده مقاله: 162 تعداد دریافت فایل اصل مقاله: 296 |
||