Generalized inverses and operator equations
نویسندگان
چکیده
منابع مشابه
Invariance properties of an operator product involving generalized inverses
Given bounded linear operators T1, T2 and T3, this paper investigates certain invariance properties of the operator product T1XT3 with respect to the choice of bounded linear operator X, where X is a generalized inverse of T2. Different types of generalized inverses are taken into account.
متن کاملEla Invariance Properties of an Operator Product Involving Generalized Inverses
Received by the editors on April 16, 2011. Accepted for publication on June 27, 2011. Handling Editor: Oskar Maria Baksalary. Department of Mathematics, Wuyi University, Jiangmen 529020, Guangdong, P.R. China ([email protected]). The work was supported by the start-up fund of Wuyi University, Jiangmen 529020, Guangdong Province. Department of Mathematics, Wuyi University, Jiangmen 529020, Guangd...
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...
متن کاملR-Matrices and Generalized Inverses
Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of adL. For generic L a generalized inverse (and indeed the Moore-Penrose inverse) is explicitly constructed. The R-matrices are in general momentum dependent and dynamical. The constructi...
متن کاملGeneralized information and maximal order of iteration for operator equations
We consider stationary iterative methods for the solution of operator equations which use "generalized information". We seek methods with maximal order provided the points of iteration are in "good position". The new concepts of order of information and "generalized" interpolatory methods are introduced. The main result states that the maximal order is equal to the order of information which de...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1979
ISSN: 0024-3795
DOI: 10.1016/0024-3795(79)90102-2