Generalized inverses and their application to applied probability problems
نویسندگان
چکیده
منابع مشابه
A Theory of Generalized Inverses Applied to Robotics
Robotics research has made extensive use of techniques based on the Moore-Penrose inverse, or generalized-inverse, of matrices. Recently, it has been pointed out how non-invariant results may, in general, be obtained applying these techniques to some areas of robotics, namely hybrid control and inverse velocity kinematics. Unfortunately, the problems are not restricted to just these particular ...
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In this article we characterize operators on Banach spaces which have the same projections related to their outer or inner generalized inverses. As corollaries, we obatin well-known results for the Drazin inverse of bounded operators.
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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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We extend the algorithm for computing {1}, {1, 3}, {1, 4} inverses and their gradients from [11] to the set of multiple-variable rational and polynomial matrices. An improvement of this extension, appropriate to sparse polynomial matrices with relatively small number of nonzero coefficient matrices as well as in the case when the nonzero coefficient matrices are sparse, is introduced. For that ...
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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...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1982
ISSN: 0024-3795
DOI: 10.1016/0024-3795(82)90218-x