Further properties of the star, left-star, right-star, and minus partial orderings
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In this article, the star, left-star, right-star and minus partial orderings, or some of them, are shown to be equivalent for certain classes of matrices.About:
This article is published in Linear Algebra and its Applications.The article was published on 2003-12-01 and is currently open access. It has received 27 citations till now. The article focuses on the topics: Star (graph theory) & Partial isometry.read more
Citations
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The diamond partial order in rings
TL;DR: The diamond partial order as mentioned in this paper is an extension of a partial order defined in a matrix setting in [J.K. Baksalary and J. Hauke, 1990].
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Further properties on the core partial order and other matrix partial orders
TL;DR: In this article, the core inverse of matrices has been studied in linear multilinear algebra and some new characterizations are obtained by using Hartwig-Spindelbck decomposition.
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Star, left-star, and right-star partial orders in Rickart ∗-rings
TL;DR: In this paper, the star, the left-star and the right-star partial orders of a ring admitting involution are studied and conditions under which these orders are equivalent to the minus partial order are obtained.
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Further results on generalized and hypergeneralized projectors
TL;DR: The notions of generalized and hypergeneralized projectors, introduced by Gros and Trenkler [J.E. Gro s, J.Gros and Gros as discussed by the authors, have been revisited in the context of matrix partial orderings.
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Further properties of generalized and hypergeneralized projectors
TL;DR: In this article, generalized and hypergeneralized projectors, introduced by Gros and Trenkler [Linear Algebra Appl. 264 (1997) 463], are revisited.
References
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The natural partial order on a regular semigroup
TL;DR: In this paper, it was shown that the natural partial order on regular semigroups is compatible with the multiplication of a semigroup if and only if the semigroup is pseudo-inverse.
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Natural structures on semigroups with involution
TL;DR: In this paper, it was shown that the proper *-semigroup axioms allow the simultaneous development of a surprisingly rich common theory of these special cases of groups and inverse semigroups.
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Some properties of matrix partial orderings
TL;DR: In this article, the authors considered the problems of inheriting certain properties under a given ordering, preserving an ordering under some matrix multiplications, relationships between an ordering among direct (or Kronecker) and Hadamard products and the corresponding orderings between the factors involved, and ordering between generalized inverses of a given matrix.
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On some characterizations of the “star” partial ordering for matrices and rank subtractivity
TL;DR: The main result of as mentioned in this paper is that Drazin's "star" partial ordering holds if and only if A ∠ B and B −A −A =(B−A)
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Left-star and right-star partial orderings
TL;DR: In this paper, two partial orderings in the set of complex matrices are introduced by combining each of the conditions A*A = A*B and AA* = BA*, which define the star partial ordering.