Extreme preservers of maximal column rank inequalities of matrix sums over semirings
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 693-703 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme properties with respect to maximal column rank inequalities of matrix sums over semirings.
We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme properties with respect to maximal column rank inequalities of matrix sums over semirings.
Classification : 15A03, 15A04, 15A45
Keywords: linear operator; rank inequality; maximal column rank.
@article{CMJ_2008_58_3_a7,
     author = {Song, Seok-Zun and Park, Kwon-Ryong},
     title = {Extreme preservers of maximal column rank inequalities of matrix sums over semirings},
     journal = {Czechoslovak Mathematical Journal},
     pages = {693--703},
     year = {2008},
     volume = {58},
     number = {3},
     mrnumber = {2455931},
     zbl = {1174.15001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a7/}
}
TY  - JOUR
AU  - Song, Seok-Zun
AU  - Park, Kwon-Ryong
TI  - Extreme preservers of maximal column rank inequalities of matrix sums over semirings
JO  - Czechoslovak Mathematical Journal
PY  - 2008
SP  - 693
EP  - 703
VL  - 58
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a7/
LA  - en
ID  - CMJ_2008_58_3_a7
ER  - 
%0 Journal Article
%A Song, Seok-Zun
%A Park, Kwon-Ryong
%T Extreme preservers of maximal column rank inequalities of matrix sums over semirings
%J Czechoslovak Mathematical Journal
%D 2008
%P 693-703
%V 58
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a7/
%G en
%F CMJ_2008_58_3_a7
Song, Seok-Zun; Park, Kwon-Ryong. Extreme preservers of maximal column rank inequalities of matrix sums over semirings. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 693-703. http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a7/

[1] Beasley, L. B., Guterman, A. E.: Rank inequalities over semirings. J. Korean Math. Soc. 42 (2005), 223-241. | DOI | MR | Zbl

[2] Beasley, L. B., Guterman, A. E.: Linear preservers of extremes of rank inequalities over semirings: Factor rank. J. Math. Sci., New York 131 (2005), 5919-5938. | DOI | MR

[3] Beasley, L. B., Guterman, A. E., Neal, C. L.: Linear preservers for Sylvester and Frobenius bounds on matrix rank. Rocky Mt. J. Math. 36 (2006), 67-80. | DOI | MR | Zbl

[4] Beasley, L. B., Lee, S.-G., Song, S.-Z.: Linear operators that preserve pairs of matrices which satisfy extreme rank properties. Linear Algebra Appl. 350 (2002), 263-272. | MR | Zbl

[5] Beasley, L. B., Pullman, N. J.: Semiring rank versus column rank. Linear Algebra Appl. 101 (1988), 33-48. | MR | Zbl

[6] Guterman, A. E.: Linear preservers for matrix inequalities and partial orderings. Linear Algebra Appl. 331 (2001), 75-87. | MR | Zbl

[7] Marsaglia, G., Styan, P.: When does $\operatorname{rank}(A+B)=\operatorname{rank}(A)+\operatorname{rank}(B)$?. Canad. Math. Bull. 15 (1972), 451-452. | DOI | MR

[8] al., P. Pierce at: A survey of linear preserver problems. Linear Multilinear Algebra 33 (1992), 1-119. | DOI

[9] Song, S.-Z.: Linear operators that preserve maximal column ranks of nonnegative integer matrices. Proc. Am. Math. Soc. 126 (1998), 2205-2211. | DOI | MR | Zbl