%0 Journal Article %T Decomposability of Weak Majorization %J Wavelet and Linear Algebra %I Vali-e-Asr university of Rafsanjan %Z 2383-1936 %A Khalooei, Fatemeh %A Ilkhanizadeh Manesh, Asma %D 2022 %\ 03/01/2022 %V 8 %N 2 %P 11-18 %! Decomposability of Weak Majorization %K Decomposability %K Doubly substochastic matrix %K Weak majorization %K Majorization %R 10.22072/wala.2021.525980.1321 %X 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