Generalized Inverses and Spectral Theory
نویسندگان
چکیده
منابع مشابه
Generalized 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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Article history: Received 20 August 2014 Accepted 3 January 2015 Available online xxxx Submitted by Y. Wei MSC: 06A06 15A09 16U99
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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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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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Abstraet--Jacobians are used in robotics for motion planning and control. They are also used in algorithms that determine linkage parameter errors of robots and in algorithms that determine pair variable corrections for accurate motion. Most applications require that the inverse of the Jacobian be obtained. The causes of singularities in Jacobians and a procedure to detect their presence are gi...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1976
ISSN: 0002-9947
DOI: 10.2307/1999728