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 -
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