Linear Preservers of Chain Majorization

Parisa Torabian

Abstract


For (n×m matrices) X, Y ∈ Mnm(R)(= Mnm), we say X is chain majorized by Y and write X ≺≺ Y if X = RY where R is a product of finitely many T-transforms. A linear operator T : Mnm → Mnm is said to be a linear preserver of the relation ≺≺ onMnm ifX≺≺Y impliesthatTX≺≺TY. Also,itissaidto be strong linear preserver if X ≺≺ Y is equivalent to T X ≺≺ T Y . In this paper we characterize linear and strong linear preservers of ≺≺.

Keywords


Doubly stochastic matrix, chain ma- jorization, left multivariate majorization, T-transform, permuta- tion, linear preserver, strong linear preserver.

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