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JOURNALS // Fundamentalnaya i Prikladnaya Matematika

Fundam. Prikl. Mat., 2004, Volume 10, Issue 2, Pages 3–21 (Mi fpm763)

Linear preservers of extremes of rank inequalities over semirings: term-rank and zero-term-rank
L. B. Beasley, A. È. Guterman, S. Yi

References

1. Beasley L. B., “Linear operators which preserve pairs on which the rank is additive”, J. Korean S.I.A.M., 2 (1998), 27–30
2. Beasley L. B., Guterman A. E., “Linear preservers of extremes of rank inequalities over semirings: The factor rank”, J. Math. Sci., 2004 (to appear)
3. Beasley L. B., Guterman A. E., “Rank inequalities over semirings”, J. Korean Math. Soc. (to appear)  mathscinet
4. Beasley L. B., Guterman A. E., Neal C. L., “Linear preservers for Sylvester and Frobenius bounds on matrix rank”, Rocky Mountain J. Math., 2004 (to appear)  mathscinet
5. Beasley L. B., Lee S.-G., Song S.-Z., “Linear operators that preserve zero-term rank of Boolean matrices”, J. Korean Math. Soc., 36:6 (1999), 1181–1190  mathscinet  zmath
6. 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  mathscinet  zmath
7. Beasley L. B., Pullman N. J., “Term rank, permanent and rook polynomial preservers”, Linear Algebra Appl., 90 (1987), 33–46  crossref  mathscinet  zmath
8. Beasley L. B., Pullman N. J., “Operators that preserve semiring matrix functions”, Linear Algebra Appl., 99 (1988), 199–216  crossref  mathscinet  zmath
9. Beasley L. B., Pullman N. J., “Linear operators that preserve term rank 1”, Proc. Roy. Irish Acad., 91 (1990), 71–78  mathscinet
10. Brualdi R., Ryser H., Combinatorial Matrix Theory, Cambridge University Press, Cambridge, 1991  mathscinet  zmath
11. Guterman A. E., “Linear preservers for matrix inequalities and partial orderings”, Linear Algebra Appl., 331 (2001), 75–87  crossref  mathscinet  zmath
12. Marsaglia G., Styan P., “When does $\mathrm{rk}(A+B)=\mathrm{rk}(A)+\mathrm{rk}(B)$?”, Canad. Math. Bull., 15:3 (1972), 451–452  crossref  mathscinet  zmath
13. Marsaglia G., Styan P., “Equalities and inequalities for ranks of matrices”, Linear and Multilinear Algebra, 2 (1974), 269–292  crossref  mathscinet  zmath
14. Minc H., Permanents, Encyclopedia in Mathematics and its Applications, 6, Addison-Wesley Publishing Company, 1978  mathscinet  zmath
15. P. Pierce and others, “A survey of linear preserver problems”, Linear and Multilinear Algebra, 33 (1992), 1–119  zmath
16. Tian Y., “Rank equalities related to outer inverses of matrices and applications”, Linear and Multilinear Algebra, 49 (2002), 269–288  crossref  mathscinet
17. Tian Y., “Upper and lower bounds for ranks of matrix expressions using generalized inverses”, Linear Algebra Appl., 355 (2002), 187–214  crossref  mathscinet  zmath


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