Geodesic
On row-sum majorization
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 1111-1121
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $\mathbb {M}_{n,m}$.
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 $\mathbb {M}_{n,m}$.
DOI : 10.21136/CMJ.2019.0084-18
Classification : 15A04, 15A21
Keywords: majorization; linear preserver; doubly stochastic matrix 
@article{10_21136_CMJ_2019_0084_18,
     author = {Akbarzadeh, Farzaneh and Armandnejad, Ali},
     title = {On row-sum majorization},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1111--1121},
     year = {2019},
     volume = {69},
     number = {4},
     doi = {10.21136/CMJ.2019.0084-18},
     mrnumber = {4039625},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0084-18/}
}
TY  - JOUR
AU  - Akbarzadeh, Farzaneh
AU  - Armandnejad, Ali
TI  - On row-sum majorization
JO  - Czechoslovak Mathematical Journal
PY  - 2019
SP  - 1111
EP  - 1121
VL  - 69
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0084-18/
DO  - 10.21136/CMJ.2019.0084-18
LA  - en
ID  - 10_21136_CMJ_2019_0084_18
ER  - 
%0 Journal Article
%A Akbarzadeh, Farzaneh
%A Armandnejad, Ali
%T On row-sum majorization
%J Czechoslovak Mathematical Journal
%D 2019
%P 1111-1121
%V 69
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0084-18/
%R 10.21136/CMJ.2019.0084-18
%G en
%F 10_21136_CMJ_2019_0084_18
Akbarzadeh, Farzaneh; Armandnejad, Ali. On row-sum majorization. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 1111-1121. doi: 10.21136/CMJ.2019.0084-18

[1] Ando, T.: Majorization, doubly stochastic matrices, and comparison of eigenvalues. Linear Algebra Appl. 118 (1989), 163-248. | DOI | MR | JFM

[2] Armandnejad, A., Heydari, H.: Linear preserving $gd$-majorization functions from $M_{n,m}$ to $M_{n,k}$. Bull. Iran. Math. Soc. 37 (2011), 215-224. | MR | JFM

[3] Bhatia, R.: Matrix Analysis. Graduate Texts in Mathematics 169, Springer, New York (1997). | DOI | MR | JFM

[4] Hasani, A. M., Radjabalipour, M.: The structure of linear operators strongly preserving majorizations of matrices. Electron. J. Linear Algebra 15 (2006), 260-268. | DOI | MR | JFM

[5] Motlaghian, S. M., Armandnejad, A., Hall, F. J.: Linear preservers of Hadamard majorization. Electron. J. Linear Algebra 31 (2016), 593-609. | DOI | MR | JFM

[6] Soleymani, M., Armandnejad, A.: Linear preservers of circulant majorization on $\mathbb{R}^n$. Linear Algebra Appl. 440 (2014), 286-292. | DOI | MR | JFM

[7] Soleymani, M., Armandnejad, A.: Linear preservers of even majorization on $M_{n,m}$. Linear Multilinear Algebra 62 (2014), 1437-1449. | DOI | MR | JFM

Cité par Sources :