@article {
author = {Khalooei, Fatemeh and Ilkhanizadeh Manesh, Asma},
title = {Decomposability of Weak Majorization},
journal = {Wavelet and Linear Algebra},
volume = {8},
number = {2},
pages = {11-18},
year = {2022},
publisher = {Vali-e-Asr university of Rafsanjan},
issn = {2383-1936},
eissn = {2476-3926},
doi = {10.22072/wala.2021.525980.1321},
abstract = {Let $x, y\in \mathbb{R}^n.$ We use the notation $x\prec_w y$ when $x$ is weakly majorized by $y$. We say that $x\prec_w y$ is decomposable at $k$ $(1\leq k < n)$ if $x\prec_w y$ has a coincidence at $k$ and $y_{k}\neq y_{k+1}$. Corresponding to this majorization we have a doubly substochastic matrix $P$. The paper presents $x\prec_w y$ is decomposable at some $k$ $(1\leq k