Reprint of: On generalized inverses and Green’s relations
نویسندگان
چکیده
منابع مشابه
On generalized inverses and Green’s relations
We study generalized inverses on semigroups by means of Green’s relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse and Moore-Penrose inverse) belong to this class. There exist many specific generalized inverses in the literature, such as the group inverse, the Moore-Penro...
متن کاملA note on generalized inverses
Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications.
متن کاملGeneralized Inverses and Applications
Fredholm’s method to solve a particular integral equation in 1903, was probably the first written work on generalized inverses. In 1906, Moore formulated the generalized inverse of a matrix in an algebraic setting, which was published in 1920, and in the thirties von Neumann used generalized inverses in his studies of continuous geometries and regular rings. Kaplansky and Penrose, in 1955, inde...
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this dissertation has six chapter and tree appendices. chapter 1 introduces the thesis proposal including description of problem, key questions, hypothesis, backgrounds and review of literature, research objectives, methodology and theoretical concepts (key terms) taken the literature and facilitate an understanding of national security, national interest and turkish- israeli relations concepts...
15 صفحه اولOn generalized inverses of singular matrix pencils
Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate s...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2012.12.002