Zero-term rank preservers of integer matrices

• Autorzy: Seok-Zun Song , Young-Bae Jun
• Języki publikacji: EN

Abstrakty

EN

The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.

Słowa kluczowe

EN

linear operator; term-rank; zero-term rank; (P,Q,B)-operator

Kategorie tematyczne

• 15A04: Linear transformations, semilinear transformations
• 15A03: Vector spaces, linear dependence, rank

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2006
• Tom: 26
• Numer: 2
• Strony: 155-161

Daty

wydano

2006

otrzymano

2005-01-25

Twórcy

autor

Seok-Zun Song

• Department of Mathematics, Cheju National University Jeju, 690-756, Republic of Korea

autor

Young-Bae Jun

• Department of Mathematics Education, Gyeongsang National University, Jinju, 660-701, Republic of Korea

Bibliografia

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• [4] R.A. Brualdi and H.J. Ryser, Combinatorial Matrix Theory, Encyclopedia of Mathematics and its Applications, Vol. 39, Cambridge University Press, Cambridge 1991.
• [5] C R. Johnson and J.S. Maybee, Vanishing minor conditions for inverse zero patterns, Linear Algebra Appl. 178 (1993), 1-15.
• [6] M. Marcus, Linear operations on matrices, Amer. Math. Monthly 69 (1962), 837-847.
• [7] H. Minc, Permanents, Encyclopedia of Mathematics and its Applications, Vol. 6, Addison-Wesley Publishing Company, Reading, Massachusetts 1978.
• [8] C.K. Li and N.K. Tsing, Linear preserver problems: A brief introduction and some special techniques, Linear Algebra Appl. 162-164 (1992), 217-235.

Identyfikatory

DOI

10.7151/dmgaa.1109