Linear preservers of rc-majorization on matrices

Mohammad Soleymani

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 4, page 1275-1288
  • ISSN: 0011-4642

Abstract

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Let A , B be n × m matrices. The concept of matrix majorization means the j th column of A is majorized by the j th column of B and this is done for all j by a doubly stochastic matrix D . We define rc-majorization that extended matrix majorization to columns and rows of matrices. Also, the linear preservers of rc-majorization will be characterized.

How to cite

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Soleymani, Mohammad. "Linear preservers of rc-majorization on matrices." Czechoslovak Mathematical Journal 74.4 (2024): 1275-1288. <http://eudml.org/doc/299660>.

@article{Soleymani2024,
abstract = {Let $A$, $B$ be $n \times m$ matrices. The concept of matrix majorization means the $j$th column of $A$ is majorized by the $j$th column of $B$ and this is done for all $j$ by a doubly stochastic matrix $D$. We define rc-majorization that extended matrix majorization to columns and rows of matrices. Also, the linear preservers of rc-majorization will be characterized.},
author = {Soleymani, Mohammad},
journal = {Czechoslovak Mathematical Journal},
keywords = {matrix majorization; linear preserver; permutation},
language = {eng},
number = {4},
pages = {1275-1288},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear preservers of rc-majorization on matrices},
url = {http://eudml.org/doc/299660},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Soleymani, Mohammad
TI - Linear preservers of rc-majorization on matrices
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 4
SP - 1275
EP - 1288
AB - Let $A$, $B$ be $n \times m$ matrices. The concept of matrix majorization means the $j$th column of $A$ is majorized by the $j$th column of $B$ and this is done for all $j$ by a doubly stochastic matrix $D$. We define rc-majorization that extended matrix majorization to columns and rows of matrices. Also, the linear preservers of rc-majorization will be characterized.
LA - eng
KW - matrix majorization; linear preserver; permutation
UR - http://eudml.org/doc/299660
ER -

References

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  1. Ando, T., 10.1016/0024-3795(89)90580-6, Linear Algebra Appl. 118 (1989), 163-248. (1989) Zbl0673.15011MR0995373DOI10.1016/0024-3795(89)90580-6
  2. Bhatia, R., 10.1007/978-1-4612-0653-8, Graduate Texts in Mathematics 169. Springer, New York (1997). (1997) Zbl0863.15001MR1477662DOI10.1007/978-1-4612-0653-8
  3. Dahl, G., Guterman, A., Shteyner, P., 10.1016/j.laa.2018.06.003, Linear Algebra Appl. 555 (2018), 201-221. (2018) Zbl1401.15039MR3834200DOI10.1016/j.laa.2018.06.003
  4. Horn, R. A., Johnson, C. R., 10.1017/CBO9780511840371, Cambridge University Press, Cambridge (1994). (1994) Zbl0801.15001MR1288752DOI10.1017/CBO9780511840371

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