The Maslov dequantization, idempotent and tropical mathematics: a brief introduction.
Litvinov, G.L. (2005)
Zapiski Nauchnykh Seminarov POMI
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Litvinov, G.L. (2005)
Zapiski Nauchnykh Seminarov POMI
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Robert W. Quackenbush (1974)
Colloquium Mathematicae
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Dula, Giora, Hilton, Peter (2003)
International Journal of Mathematics and Mathematical Sciences
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Xiaopeng Yue, Dahai Hu, Xiquan Liang (2006)
Formalized Mathematics
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This article provides definitions of idempotent, nilpotent, involutory, self-reversible, similar, and congruent matrices, the trace of a matrix and their main properties.
Ágnes Szendrei (1996)
Mathematica Slovaca
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J. Płonka (1970)
Colloquium Mathematicae
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Peter Šemrl (2007)
Banach Center Publications
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The set of all bounded linear idempotent operators on a Banach space X is a poset with the partial order defined by P ≤ Q if PQ = QP = P. Another natural relation on the set of idempotent operators is the orthogonality relation defined by P ⊥ Q ⇔ PQ = QP = 0. We briefly survey known theorems on maps on idempotents preserving order or orthogonality. We discuss some related results and open problems. The connections with physics, geometry, theory of automorphisms, and linear preserver...
E.M. Norris (1979)
Semigroup forum
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Margalida Mas Grimalt, Joan Torrens, Tomasa Calvo, Marc Carbonell (1999)
Mathware and Soft Computing
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This work is devoted to find and study some possible idempotent operators on a finite chain L. Specially, all idempotent operators on L which are associative, commutative and non-decreasing in each place are characterized. By adding one smoothness condition, all these operators reduce to special combinations of Minimum and Maximum.
H. Wang (1994)
Semigroup forum
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Saworotnow, P.P. (2003)
International Journal of Mathematics and Mathematical Sciences
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Kim, Jin Bai, Dowdy, James E. (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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