Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
linear operator; rank inequality; maximal column rank.
linear operator; rank inequality; maximal column rank.
Summary:
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.
References:
[1] Beasley, L. B., Guterman, A. E.: Rank inequalities over semirings. J. Korean Math. Soc. 42 (2005), 223-241. DOI 10.4134/JKMS.2005.42.2.223 | MR 2121497 | Zbl 1127.15001
[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 10.1007/s10958-005-0451-1 | MR 2153693
[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 10.1216/rmjm/1181069488 | MR 2228184 | Zbl 1134.15003
[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 1906757 | Zbl 1004.15025
[5] Beasley, L. B., Pullman, N. J.: Semiring rank versus column rank. Linear Algebra Appl. 101 (1988), 33-48. MR 0941294 | Zbl 0642.15002
[6] Guterman, A. E.: Linear preservers for matrix inequalities and partial orderings. Linear Algebra Appl. 331 (2001), 75-87. MR 1832488 | Zbl 0985.15018
[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 10.4153/CMB-1972-082-8 | MR 0311674
[8] al., P. Pierce at: A survey of linear preserver problems. Linear Multilinear Algebra 33 (1992), 1-119. DOI 10.1080/03081089208818176
[9] Song, S.-Z.: Linear operators that preserve maximal column ranks of nonnegative integer matrices. Proc. Am. Math. Soc. 126 (1998), 2205-2211. DOI 10.1090/S0002-9939-98-04308-1 | MR 1443409 | Zbl 0896.15009
Search
Partner of
