On row-sum majorization

Akbarzadeh, Farzaneh ; Armandnejad, Ali

Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 1111-1121.

Résumé

Let $\mathbb {M}_{n,m}$ be the set of all $n\times m$ real or complex matrices. For $A,B\in \mathbb {M}_{n,m}$, we say that $A$ is row-sum majorized by $B$ (written as $A\prec ^{\rm rs} B$) if $R(A)\prec R(B)$, where $R(A)$ is the row sum vector of $A$ and $\prec $ is the classical majorization on $\mathbb {R}^n$. In the present paper, the structure of all linear operators $T\colon \mathbb {M}_{n,m}\rightarrow \mathbb {M}_{n,m}$ preserving or strongly preserving row-sum majorization is characterized. Also we consider the concepts of even and circulant majorization on $\mathbb {R}^n$ and then find the linear preservers of row-sum majorization of these relations on $\mathbb {M}_{n,m}$.

Détail

DOI : 10.21136/CMJ.2019.0084-18

Classification : 15A04, 15A21
Keywords: majorization; linear preserver; doubly stochastic matrix