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Keywords:
majorization; linear preserver; doubly stochastic matrix
majorization; linear preserver; doubly stochastic matrix
Summary:
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 $\mathbb {M}_{n,m}$.
References:
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