TY - JOUR
ID - 251147
TI - Decomposability of Weak Majorization
JO - Wavelet and Linear Algebra
JA - WALA
LA - en
SN - 2383-1936
AU - Khalooei, Fatemeh
AU - Ilkhanizadeh Manesh, Asma
AD - Shahid Bahonar University of Kerman
AD - Assistant Professor, Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box: 7713936417, Rafsanjan, Iran
Y1 - 2022
PY - 2022
VL - 8
IS - 2
SP - 11
EP - 18
KW - Decomposability
KW - Doubly substochastic matrix
KW - Weak majorization
KW - Majorization
DO - 10.22072/wala.2021.525980.1321
N2 - 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