ON LINEAR PRESERVERS OF LGW-MAJORIZATION ON MN,M
Ali Armandnejad, Abbas Salemi · 2012
Let Mn,m be the set of all n ×m matrices with entries in F, where F is the field of real or complex numbers. For A,B ∈ Mn,m, we say that B is lgw-majorized (left generalized weakly majorized) by A if there exists an n×n g-row stochastic (generalized row stochastic) matrix R such that B = RA. In this paper, we characterize all linear operators that strongly preserve lgwmajorization on Mn,m and all linear operators that strongly preserve left weak matrix majorization on Mn. keyword: Linear preserver, strong linear preserver, g-row stochastic matrices, lgwmajorization. Subject Classification: 15A03, 15A04, 15A51.