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On Row-Sum Majorization

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Abstract

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

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Correspondence to Farzaneh Akbarzadeh or Ali Armandnejad.

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Akbarzadeh, F., Armandnejad, A. On Row-Sum Majorization. Czech Math J 69, 1111–1121 (2019). https://doi.org/10.21136/CMJ.2019.0084-18

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  • DOI: https://doi.org/10.21136/CMJ.2019.0084-18

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