TY - JOUR ID - 6350 TI - Linear preservers of two-sided matrix majorization JO - Wavelet and Linear Algebra JA - WALA LA - en SN - 2383-1936 AU - Khalooei, F. AD - Department of Mathmatics, Faculty of Mathmatics, Shahid Bahonar University of Kerman, Kerman, Islamic Republic of Iran Y1 - 2014 PY - 2014 VL - 1 IS - 1 SP - 43 EP - 50 KW - Linear preservers KW - Matrix majorization KW - Row stochastic matrix DO - N2 - For vectors X, Y ∈ Rn, it is said that X is left matrix majorized by Y if for some row stochastic matrix R; X = RY. The relation X ∼` Y, is defined as follows: X ∼` Y if and only if X is left matrix majorized by Y and Y is left matrix majorized by X. A linear operator T : Rp → Rn is said to be a linear preserver of a given relation ≺ if X ≺ Y on Rp implies that T X ≺ TY on Rn. The linear preservers of ≺` from Rp to Rn are characterized before. In this parer we characterize the linear preservers of ∼` from Rp to Rn, p ≥ 3. In fact we show that the linear preservers of ∼` from Rp to Rn are the same as the linear preservers of ≺` from Rp to Rn, but for p = 2, they are not the same. UR - https://wala.vru.ac.ir/article_6350.html L1 - https://wala.vru.ac.ir/article_6350_cfc0204b394816145bc22b5af538dfde.pdf ER -