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EXTREME PRESERVERS OF TERM RANK INEQUALITIES OVER NONBINARY BOOLEAN SEMIRING

허성희|송석준|비어슬리
대한수학회 (The Korean Mathematical Society)|2014.01|대한수학회지 (Journal of the KMS)|제51권 제1호|pp. 113-123

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참고문헌

키워드

linear operatorterm ranknonbinary Boolean semiring.
주제분류수학

초록

The term rank of a matrix A over a semiring S is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.

Abstract

The term rank of a matrix A over a semiring S is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.

참고문헌 (12)

  1. LeRoy B. Beasley, "RANK INEQUALITIES OVER SEMIRINGS", 대한수학회지, 42(2), pp.33~51 (2005), 대한수학회
  2. L. B. Beasley, "Linear preservers of extremes of rank inequalities over semirings", J. Math. Sciences, 131(5), pp.5919~5938 (2005)
  3. L. B. Beasley, "Linear preservers of extremes of rank inequalities over semirings: row and column ranks", Linear Algebra and Its Applications, 413(2-3), pp.495~509 (2006)
  4. L. B. Beasley, "Linear operators that preserve pairs of matrices which satisfy extreme rank properties", Linear Algebra Appl, pp.263~272 (2002)
  5. L. B. Beasley, "Term rank, permanent and rook polynomial preservers", Linear Algebra Appl, 90, pp.33~46 (1987)
  6. L. B. Beasley, "Preservers of term ranks of symmetric matrices", Linear Algebra Appl, 436(6), pp.1727~1738 (2012)
  7. K. T. Kang, "Linear preservers of term ranks of matrices over semirings", Linear Algebra Appl, 436(7), pp.1850~1862 (2012)
  8. S. Kirkland, "Linear operators preserving invariants of nonbinary matrices", Linear and Multilinear Algebra, 33(3-4), pp.295~300 (1992)
  9. C. K. Li, "Linear preserver problems", Amer. Math. Monthly, 108(7), pp.591~605 (2001)
  10. S. Pierce, "A survey of linear preserver problems contents", Linear and Multilinear Algebra, 33(1-2), pp.1~119 (1992)
  11. S. Z. Song, "Linear Preservers of Extremes of Matrix Pairs Over Nonbinary Boolean Algebra", Bull. Malays. Math. Sci. Soc, 36(1), pp.73~81 (2013)
  12. 송석준, "Extreme sets of rank inequalities over Boolean matrices and their preservers", 대한수학회논문집, 28(1), pp.1~9 (2013), 대한수학회

관련 논문AI추천

EXTREME PRESERVERS OF MAXIMAL COLUMN RANK INEQUALITIES OF MATRIX MULTIPLICATIONS OVER SEMIRINGS박권룡, 송석준, L. Hernandez Encinas대한수학회 · 대한수학회지2010 · 제47권 제1호Extreme sets of rank inequalities over Boolean matrices and their preservers강문환, 송석준, 전영배대한수학회 · 대한수학회논문집2013 · 제28권 제1호Linear transformations that preserve term rank between different matrix spaces송석준, LeRoy B. Beasley대한수학회 · 대한수학회지2013 · 제50권 제1호Linear preservers of spanning column rank of matrix sums over semirings송석준대한수학회 · 대한수학회지2008 · 제45권 제2호Characterizations of Zero-Term Rank Preservers of Matrices over Semirings강경태, 송석준, 비어슬리, Luis Hernandez Encinas경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제4호Linear preservers of spanning column rank of matrix products over semirings송석준, 전영배, 천기상대한수학회 · 대한수학회지2008 · 제45권 제4호

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