TY - JOUR
ID - 18317
TI - The structure of strongly linear preservers of degree majorization
JO - Journal of Advanced Mathematical Modeling
JA - JAMM
LA - en
SN - 2251-8088
AU - Sayyari, Yamin
AU - Mohammadhasani, Ahmad
AU - Dehghanian, Mehdi
AD - Department of Mathematics, Sirjan University of Technology, Sirjan, Iran
Y1 - 2023
PY - 2023
VL - 13
IS - 1
SP - 79
EP - 91
KW - Majorization&lrm
KW - &lrm
KW - m&lrm
KW - ultivariate majorization&lrm
KW - degree majorization&lrm
KW - strongly linear preserver
DO - 10.22055/jamm.2023.42660.2122
N2 - 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 $D$. 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 $\mathbb{R}^n$.
UR - https://jamm.scu.ac.ir/article_18317.html
L1 - https://jamm.scu.ac.ir/article_18317_c8a8c51fa7036db27edbef08fb41a5c9.pdf
ER -