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2006 | 26 | 2 | 155-161
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Zero-term rank preservers of integer matrices

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Abstrakty
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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.
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Twórcy
  • Department of Mathematics, Cheju National University Jeju, 690-756, Republic of Korea
  • Department of Mathematics Education, Gyeongsang National University, Jinju, 660-701, Republic of Korea
Bibliografia
  • [1] L.B. Beasley and N.J. Pullman, Term-rank, permanent and rook-polynomial preservers, Linear Algebra Appl. 90 (1987), 33-46.
  • [2] L.B. Beasley, S.Z. Song and S.G. Lee, Zero-term rank preserver, Linear and Multilinear Algebra. 48 (2) (2000), 313-318.
  • [3] L.B. Beasley, Y.B. Jun and S.Z. Song, Zero-term ranks of real matrices and their preserver, Czechoslovak Math. J. 54 (129) (2004), 183-188.
  • [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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1109
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