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Strictly sub row Hadamard majorization | ||
| Journal of Mahani Mathematical Research | ||
| دوره 11، شماره 1 - شماره پیاپی 21، فروردین 2022، صفحه 159-168 اصل مقاله (485.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.18576.1177 | ||
| نویسنده | ||
| Abbas Askarizadeh* | ||
| Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran | ||
| چکیده | ||
| Let $\textbf{M}_{m,n}$ be the set of all $m$-by-$n$ real matrices. A matrix $R$ in $\textbf{M}_{m,n}$ with nonnegative entries is called strictly sub row stochastic if the sum of entries on every row of $R$ is less than 1. For $A,B\in\textbf{M}_{m,n}$, we say that $A$ is strictly sub row Hadamard majorized by $B$ (denoted by $A\prec_{SH}B)$ if there exists an $m$-by-$n$ strictly sub row stochastic matrix $R$ such that $A=R\circ B$ where $X \circ Y$ is the Hadamard product (entrywise product) of matrices $X,Y\in\textbf{M}_{m,n}$. In this paper, we introduce the concept of strictly sub row Hadamard majorization as a relation on $\textbf{M}_{m,n}$. Also, we find the structure of all linear operators $T:\textbf{M}_{m,n} \rightarrow \textbf{M}_{m,n}$ which are preservers (resp. strong preservers) of strictly sub row Hadamard majorization. | ||
| کلیدواژه‌ها | ||
| Linear preserver؛ Strong linear preserver؛ Strictly sub row stochastic matrices | ||
| مراجع | ||
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[1] C. Davis, The norm of the Schur product operation, Numerische Mathematik, vol. 4, no 1. (1962) 343-344.
[2] B. Cyganek, Obeject detection and recognition in digital images (theory and practice), A John Wiley and Sons, 2013.
[3] P. H. George, Hadamard product and multivariate statistical analysis, Linear Algebra and its Applications vol. 6 (1973) 217-240 .
[4] R. A. Horn and C. R. Johnson, Matrix analysis, Cambridge University Press, 2012.
[5] S. M. Motlaghian, A. Armandnejad and F. J. Hall, Linear preservers of Hadamard majorization, Electronic Journal of Linear Algebra, vol 31. (2016) 593-609. | ||
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