Linear preservers of left matrix majorization
Fatemeh Khalooei, Mehdi Radjabalipour, Torabian Parisa · Electronic Journal of Linear Algebra · 2008
For X, Y ∈ Mnm(R) (= Mnm), we say that Y is left (resp.right) matrix majorized by X and write Y ≺ ℓ X (resp.Y ≺r X) if Y = RX (resp.Y = XR) for some row stochastic matrix R. A linear operator T : Mnm → Mnm is said to be a linear preserver of a given relation ≺ on Mnm if Y ≺ X implies that T Y ≺ T X.The linear preservers of ≺ ℓ or ≺r are fully characterized by A.M. Hasani and M. Radjabalipour.Here, we launch an attempt to extend their results to the case where the domain and the codomain of T are not necessarily identical.We begin by characterizing linear preservers T : M p1 → M n1 of ≺ ℓ .