# Linear preservers of two-sided matrix majorization

Document Type : Research Paper

Author

Department of Mathmatics, Faculty of Mathmatics, Shahid Bahonar University of Kerman, Kerman, Islamic Republic of Iran

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

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