@article { author = {Khalooei, F.}, title = {Linear preservers of two-sided matrix majorization}, journal = {Wavelet and Linear Algebra}, volume = {1}, number = {1}, pages = {43-50}, year = {2014}, publisher = {Vali-e-Asr university of Rafsanjan}, issn = {2383-1936}, eissn = {2476-3926}, doi = {}, abstract = {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.}, keywords = {Linear preservers,Matrix majorization,Row stochastic matrix}, url = {https://wala.vru.ac.ir/article_6350.html}, eprint = {https://wala.vru.ac.ir/article_6350_cfc0204b394816145bc22b5af538dfde.pdf} }