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MATRIX REPRESENTATIONS OF AMPLE SEMIGROUPS
Journal of Algebra and Its Applications, 2013An adequate semigroup S is said to be ample if for any e2 = e, a ∈ S, ae = (ae)†a and ea = a(ea)*. It is well known that inverse semigroups are ample semigroups. The purpose of this paper is to study matrix representations of an ample semigroup. Some properties of ample semigroups are obtained.
Guo, Xiaojiang, Shum, K. P.
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MATRIX PROBLEMS AND INTEGRAL REPRESENTATIONS
Mathematics of the USSR-Izvestiya, 1974Given a linear matrix problem, an order is constructed whose representations are classified by the matrices of this problem. It is shown that problems about representations of partially ordered sets are included in this scheme.
Drozd, Ju. A. +2 more
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2007
There are several ways of characterizing nonnegative polynomials that may be interesting for a mathematician. However, not all of them are appropriate for computational purposes, by “computational” understanding primarily optimization methods. Nonnegative polynomials have a basic property extremely useful in optimization: They form a convex set. So, an
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There are several ways of characterizing nonnegative polynomials that may be interesting for a mathematician. However, not all of them are appropriate for computational purposes, by “computational” understanding primarily optimization methods. Nonnegative polynomials have a basic property extremely useful in optimization: They form a convex set. So, an
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Similarity Matrix Representations
1974As we have seen in the previous chapters, cluster analysis can be discussed either in terms of the distance matrix D of all interpoint distances among the n objects or the similarity matrix S. In this chapter we will discuss some aspects regarding the representation of clustering results or of similarity or distance matrices.
Patrick L. Odell, Benjamin S. Duran
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Density Matrix Representations
American Journal of Physics, 1962The relations between the ordinary density matrix, the density matrix in the coordinate representation, the Löwdin density matrices, the Dirac density matrix, and other density matrices are traced. The roles of pure and mixed cases, equilibrium and nonequilibrium situations, and single- and many-body representations are considered.
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