The Structure of linear preservers of left matrix majorization on R^T
Fatemeh Khalooei, Abbas Salemi · Electronic Journal of Linear Algebra · 2009
For vectors X, Y ∈ R n , Y is said to be left matrix majorized by X (Y ≺ ℓ X) if for some row stochastic matrix R, Y = RX.A linear operator T : R p → R n is said to be a linear preserver of ≺ ℓ if Y ≺ ℓ X on R p implies that T Y ≺ ℓ T X on R n .The linear operators T : R p → R n (n < p(p-1)) which preserve ≺ ℓ have been characterized.In this paper, linear operators T : R p → R n which preserve ≺ ℓ are characterized without any condition on n and p.