| Title:
|
G-tridiagonal majorization on $\textbf {M}_{n,m}$ (English) |
| Author:
|
Mohammadhasani, Ahmad |
| Author:
|
Sayyari, Yamin |
| Author:
|
Sabzvari, Mahdi |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
395-405 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For $X,Y\in \textbf {M}_{n,m}$, it is said that $X$ is \emph {g-tridiagonal} majorized by $Y$ (and it is denoted by $X\prec _{gt}Y$) if there exists a tridiagonal g-doubly stochastic matrix $A$ such that $X=AY$. In this paper, the linear preservers and strong linear preservers of $\prec _{gt}$ are characterized on $\textbf {M}_{n,m}$. (English) |
| Keyword:
|
G-doubly stochastic matrix |
| Keyword:
|
gt-majorization |
| Keyword:
|
(strong) linear preserver |
| Keyword:
|
tridiagonal matrices. |
| MSC:
|
15A04 |
| MSC:
|
15A21 |
| idZBL:
|
Zbl 07484376 |
| idMR:
|
MR4355421 |
| . |
| Date available:
|
2022-01-10T10:03:56Z |
| Last updated:
|
2022-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149325 |
| . |
| Reference:
|
[1] Armandnejad, A., Gashool, Z.: Strong linear preservers of g-tridiagonal majorization on $\mathbb R^n$.Electronic Journal of Linear Algebra, 123, 2012, 115-121, MR 2889575 |
| Reference:
|
[2] Armandnejad, A., Mohtashami, S., Jamshidi, M.: On linear preservers of g-tridiagonal majorization on $\mathbb {R}^{n}$.Linear Algebra and its Applications, 459, 2014, 145-153, MR 3247220, 10.1016/j.laa.2014.06.050 |
| Reference:
|
[3] Beasley, L.B., Lee, S.-G., Lee, Y.-H.: A characterization of strong preservers of matrix majorization.Linear Algebra and its Applications, 367, 2003, 341-346, MR 1976930, 10.1016/S0024-3795(02)00657-2 |
| Reference:
|
[4] Bahatia, R.: Matrix Analysis.1997, Springer-Verlag, New York, |
| Reference:
|
[5] Brualdi, R.A., Dahl, G.: An extension of the polytope of doubly stochastic matrices.Linear and Multilinear Algebra, 6, 3, 2013, 393-408, MR 3003432, 10.1080/03081087.2012.689980 |
| Reference:
|
[6] Chiang, H., Li, C.K.: Generalized doubly stochastic matrices and linear preservers.Linear and Multilinear Algebra, 53, 2005, 1-11, MR 2114138, 10.1080/03081080410001681599 |
| Reference:
|
[7] Hasani, A.M., Radjabalipour, M.: The structure of linear operators strongly preserving majorizations of matrices.Electronic Journal of Linear Algebra, 15, 2006, 260-268, MR 2255479, 10.13001/1081-3810.1236 |
| Reference:
|
[8] Hasani, A.M., Radjabalipour, M.: On linear preservers of (right) matrix majorization.Linear Algebra and its Applications, 423, 2007, 255-261, MR 2312405, 10.1016/j.laa.2006.12.016 |
| Reference:
|
[9] Marshall, A.W., Olkin, I., Arnold, B.C.: Inequalities: Theory of majorization and its applications.2011, Springer, New York, MR 2759813 |
| . |
