On Witt S Theorem For Nonalternating Symmetric Bilinear Forms Over A Field Of Characteristic 2
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On Witt S Theorem For Nonalternating Symmetric Bilinear Forms Over A Field Of Characteristic 2
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Author : Vera Pless
language : en
Publisher:
Release Date : 1965
On Witt S Theorem For Nonalternating Symmetric Bilinear Forms Over A Field Of Characteristic 2 written by Vera Pless and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Bilinear forms categories.
The purpose of this note Is to show that an analogue to Witt's theorem holds for a non-degenerate, non-alternating, symmetric bilinear form f over a field K of characteristic 2 where f(x, x) takes its values in a subfield K* such that K contains the square root of any element in K*. As is known, [2, p. 171] Witt's theorem does not hold in general for a field of characteristic 2. However, the following shows that an isometry of subspace can be extended if it leaves a certain unique vector invariant. The invariants of a subspace of V with respect to the orthogonal group are determined.
Quadratic Forms In Infinite Dimensional Vector Spaces
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Author : H. Gross
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Quadratic Forms In Infinite Dimensional Vector Spaces written by H. Gross and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Science categories.
For about a decade I have made an effort to study quadratic forms in infinite dimensional vector spaces over arbitrary division rings. Here we present in a systematic fashion half of the results found du ring this period, to wit, the results on denumerably infinite spaces (" NO-forms'''). Certain among the results included here had of course been published at the time when they were found, others appear for the first time (the case, for example, in Chapters IX, X , XII where I in clude results contained in the Ph.D.theses by my students W. Allenspach, L. Brand, U. Schneider, M. Studer). If one wants to give an introduction to the geometric algebra of infinite dimensional quadratic spaces, a discussion of N-dimensional O spaces ideally serves the purpose. First, these spaces show a large number of phenomena typical of infinite dimensional spaces. Second, most proofs can be done by recursion which resembles the familiar pro cedure by induction in the finite dimensional situation. Third, the student acquires a good feeling for the linear algebra in infinite di mensions because it is impossible to camouflage problems by topological expedients (in dimension NO it is easy to see, in a given case, wheth er topological language is appropriate or not).
Government Wide Index To Federal Research Development Reports
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Author :
language : en
Publisher:
Release Date : 1965
Government Wide Index To Federal Research Development Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Government publications categories.
Oar Quarterly Index Of Current Research Results
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Author : United States. Air Force. Office of Aerospace Research
language : en
Publisher:
Release Date : 1965
Oar Quarterly Index Of Current Research Results written by United States. Air Force. Office of Aerospace Research and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Aeronautics, Military categories.
Oar Cumulative Index Of Research Results
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Author : United States. Air Force. Office of Aerospace Research
language : en
Publisher:
Release Date : 1965
Oar Cumulative Index Of Research Results written by United States. Air Force. Office of Aerospace Research and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Aeronautics categories.
Oar Cumulative Index Of Research Results
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Author :
language : en
Publisher:
Release Date :
Oar Cumulative Index Of Research Results written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Aeronautics categories.
Characteristic Frequencies From Infrared And Elastic Data
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Author : Johannes N. Plendl
language : en
Publisher:
Release Date : 1965
Characteristic Frequencies From Infrared And Elastic Data written by Johannes N. Plendl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Dielectrics categories.
Characteristic Wave Cataloguing For Ray Path Determination
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Author : Yūji Inoue
language : en
Publisher:
Release Date : 1965
Characteristic Wave Cataloguing For Ray Path Determination written by Yūji Inoue and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Geomagnetism categories.
Wave cataloguing suitable for ray tracing of a pulsed wave packet in a weakly-dissipative, horizontallystratified magnetoionic medium is described, Particular attention is devoted to the cataloguing of the various characteristic waves so that the influence of the local ionization density and collision frequency can be understood. The procedure presented is applicable under general incident conditions and complex refractive index surfaces. The Booker quartic equation is used to derive the unambiguous wave normals and wave identification is obtained from the dispersion equation. A modified CMA. diagram including collisions is illustrated. (Author).
Distortion Of A Magnetic Field By The Motion Of A Cylindrical Conductor
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Author : Joseph G. Kelley
language : en
Publisher:
Release Date : 1965
Distortion Of A Magnetic Field By The Motion Of A Cylindrical Conductor written by Joseph G. Kelley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Cylinders categories.
Motion of a conductor relative to a magnetic field distorts the field. This paper considers a cylindrical slug moving in a two-dimensional magnetic field, represented by the vector potential A sub 0 theta, where the partial derivative of A sub 0 with respect to theta = 0. Maxwell's equations are solved for the distorted potential A theta in the form of a rapidly converging series A = & A sub n. The A sub n's are given in a form suitable for evaluation by a digital computer. The nonequivalence of the apparently analogous problem of a stationary slug in a time-varying field is noted and discussed. (Author).
An Algorithm For The Deformation Method Of Quadratic Programming
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Author : Roger Even Bove
language : en
Publisher:
Release Date : 1965
An Algorithm For The Deformation Method Of Quadratic Programming written by Roger Even Bove and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Algorithms categories.
The following paper represents work to date on the deformation method for quadratic programming and thus may be regarded as a sequel to Zahl, S. (1964) A Deformation Method for Quadratic Programming, Research Note AFCRL-63-132. It gives an explanation of a modified Iverson programming language and uses this to give a detailed algorithm for the Zahl Deformation Method of Quadratic Programming.