Linear mappings preserving coincidence of factorized and boundary ranks of matrices over semirings
Tóm tắt
A problem of characterization of linear bijective mappings preserving coincidence of factorized and boundary ranks over a semiring is considered. A complete classification of those mappings over antinegative commutative rings with a unit and without divisors of zero is obtained.
Tài liệu tham khảo
K. Glazek, A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences (Kluwer Academic Publishers, 2002).
A Survey of Linear Preserver Problems. Linear and Multilinear Algebra, Ed. by C.-K. Li, S. Pierce, and N.-K. Tsing. 33, (1992).
V. N. Sachkov and V. E. Tarakanov, Progress in Theoretical and Applied Discrete Mathematics, Vol. 2: Combinatorial Calculus of Nonnegative Matrices (TVP, Moscow, 2000).
D. König, Theorie der endlichen und enendlichen eraphen. Kombinatorische Topologie der Streckenkomplexe (Akad. Verlag M.B.H., Leipzig, 1936).
L. B. Beasley and A. E. Guterman, “Linear Preservers of Extremes of Rank Inequalities over Semirings: Factor Rank,” J. Math. Sci. (N.Y.) 131(5), 5919 (2005).