Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-808813120230622The structure of strongly linear preservers of degree majorizationThe structure of strongly linear preservers of degree majorization79911831710.22055/jamm.2023.42660.2122FAYaminSayyariDepartment of Mathematics, Sirjan University of Technology, Sirjan, IranAhmadMohammadhasaniDepartment of Mathematics, Sirjan University of Technology, Sirjan, IranMehdiDehghanianDepartment of Mathematics, Sirjan University of Technology, Sirjan, IranJournal Article20230101A square matrix $D$ is called a doubly stochastic matrix if all its entries are non-negative and the sum of the entries of each row is equal to the sum of the entries of each column and is equal to one. For each linear and non-zero vector $x = (x_1, \ldots, x_n)$, we define the degree of $x$ as the largest number $i$ such that $x_i$ is non-zero and the degree of vector zero is zero. We say that a vector $x$ is degree majorized by $y$ and denote by $x\prec_{deg} y$ if the degree of $x$ is greater than or equal to the degree of $y$ and $x = yD$ for some doubly stochastic matrix $D$. <br /><br />In this paper, we obtain the structure of all linear preservers of degree majorization on space $\mathbb{R}^2$. Also, we find the structure of all strong linear preservers of degree majorization on real vector spaces $\mathbb{R}^n$.A square matrix $D$ is called a doubly stochastic matrix if all its entries are non-negative and the sum of the entries of each row is equal to the sum of the entries of each column and is equal to one. For each linear and non-zero vector $x = (x_1, \ldots, x_n)$, we define the degree of $x$ as the largest number $i$ such that $x_i$ is non-zero and the degree of vector zero is zero. We say that a vector $x$ is degree majorized by $y$ and denote by $x\prec_{deg} y$ if the degree of $x$ is greater than or equal to the degree of $y$ and $x = yD$ for some doubly stochastic matrix $D$. <br /><br />In this paper, we obtain the structure of all linear preservers of degree majorization on space $\mathbb{R}^2$. Also, we find the structure of all strong linear preservers of degree majorization on real vector spaces $\mathbb{R}^n$.https://jamm.scu.ac.ir/article_18317_c8a8c51fa7036db27edbef08fb41a5c9.pdf