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Rank-preserving operators of nonnegative integer matrices

강경태|전영배|송석준
대한수학회 (The Korean Mathematical Society)|2005.10|대한수학회논문집 (Communications of the KMS)|제20권 제4호|pp. 671-683

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주제분류수학

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Abstract

The set of all m × n matrices with entries in Z+ is de noted by Mm￡n(Z+). We say that a linear operator T on Mm￡n(Z+) is a (U, V )-operator if there exist invertible matrices U ∈ Mm￡m(Z+) and V ∈ Mn￡n(Z+) such that either T (X)= UXV for all X in Mm￡n(Z+), or m = n and T (X)= UXtV for all X in Mm￡n(Z+). In this paper we show that a linear operator T preserves the rank of matrices over the nonnegative integers if and only if T is a (U, V ) operator. We also obtain other characterizations of the linear oper ator that preserves rank of matrices over the nonnegative integers.

참고문헌 (9)

  1. "Boolean rank preserving operators and Boolean rank-1 spaces", 59, pp.55~77 (1984)
  2. "Fuzzy rank-preserving operators", 73, pp.197~211 (1986)
  3. "A comparison of nonnegative real ranks and their preservers", 31, pp.37~46 (1992)
  4. "Nonnegative Matrices in the Mathematical Sci ences" (1979)
  5. "Linear transformations on matrices", pp.343~345 (1981)
  6. "Linear transformations on algebras of matrices", 11, pp.61~66 (1959)
  7. "Transformations on tensor product spaces", 9, pp.1215~1221 (1959)
  8. "Linear operators that preserve maximal column ranks of nonnegative integer matrices", 126, pp.2205~2211 (1998)
  9. "Transformations on tensor spaces", 23, pp.613~620 (1967)

관련 논문AI추천

Maximal column rank preservers of integer matrices강경태, 송석준대한수학회 · 대한수학회논문집2007 · 제22권 제2호Factor Rank and Its Preservers of Integer Matrices강경태, Seok- Zun Song경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제4호Rank preserver of Boolean matrices강경태, 송석준, 전영배대한수학회 · 대한수학회보2005 · 제42권 제3호Rank and perimeter preservers of boolean rank-1 matrices송석준, Gi-Sang Cheon, LeRoy B. Beasley, Young-Bae Jun대한수학회 · 대한수학회지2004 · 제41권 제2호Maximal column ranks and their preservers of Matrices Over Max Algebra강경태, 송석준대한수학회 · 대한수학회지2003 · 제40권 제6호Sets of Integer Matrix Pairs Derived from Row Rank Inequalities and Their Preservers송석준, 전영배경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제2호

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