On linear preservers of sgut-majorization on Mn,m

‎Let Mn,m be the set of n-by-m‎ ‎matrices with entries in the field of real numbers‎. ‎A matrix R in Mn=Mn,n is a generalized row substochastic matrix (g-row substochastic‎, ‎for short) if Re≤e‎, ‎where e=(1,1,…,1)t‎. ‎For X, Y∈Mn,m‎, ‎X is said to be sgut-majorized by Y (denoted by X‎‎≺sgutY) if there exists an n-by-n upper triangular g-row substochastic matrix R such that X=RY‎. ‎This paper characterizes all‎ ‎linear preservers and strong linear preservers of ≺sgut on Rn and Mn,m respectively‎.