ArticleOriginal scientific text

Title

Zero-term rank preservers of integer matrices

Authors 1, 2

Affiliations

  1. Department of Mathematics, Cheju National University Jeju, 690-756, Republic of Korea
  2. Department of Mathematics Education, Gyeongsang National University, Jinju, 660-701, Republic of Korea

Abstract

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.

Keywords

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

Bibliography

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Pages:
155-161
Main language of publication
English
Received
2005-01-25
Published
2006
Exact and natural sciences