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Boolean regular matrices and their strongly preservers
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An m×n Boolean matrix A is called regular if there exists an m×n Boolean matrix X such that AXA=A. We have characterizations of Boolean regular matrices. We also determine the linear operators that strongly preserve Boolean regular matrices.
Abstract
An m×n Boolean matrix A is called regular if there exists an m×n Boolean matrix X such that AXA=A. We have characterizations of Boolean regular matrices. We also determine the linear operators that strongly preserve Boolean regular matrices.
참고문헌 (10)
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- K. H. Kim, "Boolean Matrix Theory and Applications, Pure and Applied Mathematics" (1982), Marcel Dekker
- R. D. Luce, "A note on Boolean matrix theory", Proc. Amer. Math. Soc, 3, pp.382~388 (1952)
- E. H. Moore, "General analysis, Part I", Mem. of Amer. Phil. Soc, 1 (1935)
- R. J. Plemmons, "Generalized inverses of Boolean relation matrices", SIAM J. Appl.Math., 20, pp.426~433 (1971)
- P. S. S. N. V. Prasada Rao, "On generalized inverses of Boolean matrices", Linear Algebra and Appl, 11(2), pp.135~153 (1975)
- D. E. Rutherford, "Inverses of Boolean matrices", Proc. Glasgow Math. Assoc., 6, pp.49~53 (1963)
- S. Z. Song, "Linear operators that preserve column rank of Boolean matrices", Proc. Amer. Math. Soc., 119(4), pp.1085~1088 (1993)
- 송석준, "Linear maps that preserve commuting pairs of matrices over general boolean algebra", 대한수학회지, 43(1), pp.77~86 (2006), 대한수학회
관련 논문AI추천
LINEAR PRESERVERS OF BOOLEAN RANK BETWEEN DIFFERENT MATRIX SPACES강경태, 송석준, Leroy B. Beasley대한수학회 · 대한수학회지2015 · 제52권 제3호Spanning column ranks of non-binary Boolean matrices and their preservers강경태, 송석준대한수학회 · 대한수학회지2019 · 제56권 제2호Extreme sets of rank inequalities over Boolean matrices and their preservers강문환, 송석준, 전영배대한수학회 · 대한수학회논문집2013 · 제28권 제1호CHARACTERIZATIONS OF BOOLEAN RANK PRESERVERS OVER BOOLEAN MATRICES강경태, 송석준, 비어슬리한국수학교육학회 · 이론수학과 교직수학2014 · 제21권 제2호CHARACTERIZATIONS OF THE COLUMN RANK PRESERVERS OF BOOLEAN MATRICESK-T Kang, S-Z Song장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제3호Linear preservers of Boolean nilpotent matrices강경태, 송석준, 전영배대한수학회 · 대한수학회지2006 · 제43권 제3호
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