논문KCI 등재
Linear preservers of spanning column rank of matrix sums over semirings
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초록
The spanning column rank of an m × n matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix pairs which satisfy additive properties with respect to spanning column rank of matrices over semirings.
Abstract
The spanning column rank of an m × n matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix pairs which satisfy additive properties with respect to spanning column rank of matrices over semirings.
참고문헌 (8)
- LeRoy B. Beasley, "RANK INEQUALITIES OVER SEMIRINGS", 대한수학회보, 42(2), pp.33~51 (2005), 대한수학회
- L. B. Beasley, "Linear preservers of extremes of rank inequalities over semirings: Factor rank", Journal of Mathematical Sciences (New York), 131, pp.5919~5938 (2005)
- L. B. Beasley, "Linear operators that preserve pairs of matrices which satisfy extreme rank properties", Linear Algebra and its Applications, 350, pp.263~272 (2002)
- L. B. Beasley, "Semiring rank versus column rank", Linear Algebra and its Applications, 101, pp.33~48 (1988)
- G. Marsaglia, "Equalities and inequalities for ranks of matrices", Linear and Multilinear Algebra, 2, pp.269~292 (1974)
- S. Pierce, "A Survey of Linear Preserver Problems", Linear and Multilinear Algebra, 33(1), pp.1~129 (1992)
- S. Z. Song, "Spanning column ranks and their preservers of nonnegative matrices", Linear Algebra and its Applications, 254, pp.485~495 (1997)
- 송석준, "Linear maps that preserve commuting pairs of matrices over general boolean algebra", 대한수학회보, 43(1), pp.77~86 (2006), 대한수학회
관련 논문AI추천
Linear preservers of spanning column rank of matrix products over semirings송석준, 전영배, 천기상대한수학회 · 대한수학회지2008 · 제45권 제4호EXTREME PRESERVERS OF MAXIMAL COLUMN RANK INEQUALITIES OF MATRIX MULTIPLICATIONS OVER SEMIRINGS박권룡, 송석준, L. Hernandez Encinas대한수학회 · 대한수학회지2010 · 제47권 제1호Characterizations of Zero-Term Rank Preservers of Matrices over Semirings강경태, 송석준, 비어슬리, Luis Hernandez Encinas경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제4호Linear transformations that preserve term rank between different matrix spaces송석준, LeRoy B. Beasley대한수학회 · 대한수학회지2013 · 제50권 제1호Spanning column ranks of non-binary Boolean matrices and their preservers강경태, 송석준대한수학회 · 대한수학회지2019 · 제56권 제2호EXTREME PRESERVERS OF TERM RANK INEQUALITIES OVER NONBINARY BOOLEAN SEMIRING송석준, 허성희, 비어슬리대한수학회 · 대한수학회지2014 · 제51권 제1호
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