@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