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Livres Livres 1 - 10 sur 12 pour Let V be a finite dimensional vector space over a field F..
" Let V be a finite dimensional vector space over a field F. "
The Book of Involutions - Page 1
publié par - 1998 - 593 pages
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Fields and Rings

Irving Kaplansky - 1972 - 206 pages
...F, then X- 1 is in A, so that Xs = s(X- 1), which lies in S. THEOREM 29. Let G be a torsion group. Let V be a finite -dimensional vector space over a field F. If F has characteristic p, assume also that G has no elements of order p. Then any representation of...
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Modules and Rings

John Dauns - 1994 - 442 pages
...viewed as column vectors, then Endz A, which consists of 2 x 2 matrices over Z, is noncommutative. 3. Let V be a finite dimensional vector space over a field F and T: F— » F, t; -» t;T; veV, a linear transformation. Then V is a right module over the ring...
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Fundamental Structures of Algebra and Discrete Mathematics

Stephan Foldes - 1994 - 344 pages
...represent the data, use the fact that a flat h"l(y) is fully determined by y and the matrix of h.] 2. Let V be a finite dimensional vector space over a field F. Show that ACV is an affine flat if and only if every linear combination of vectors v,. e A with CXQ...
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Duality in Analytic Number Theory

Peter D. T. A. Elliott - 1997 - 341 pages
...defined from the inside by a point locus, and from the outside by a line envelope. 2. Dual spaces. Let V be a finite dimensional vector space over a field F. The dual of V is the vector space of linear maps of V into F. The space V and its dual, V , are isomorphic....
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Finite Group Theory

M. Aschbacher - 2000 - 304 pages
...prime characteristic p and * an element of order p in GL(V). Assume n > p. Prove dim(CV(*))> 1. 9. Let V be a finite dimensional vector space over a field F, / a nontrivial sesquilinear form on V with respect to an automorphism в of finite order m, and G =...
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Linear Algebra

Max Fogiel - 2000 - 214 pages
...\_x + 2y x — 3y \2x + y [x-ïy (E) 3jc - y 6. We define a bilinear form in the following manner: Let V be a finite dimensional vector space over a field F. A bilinear form b(v; v ) is a function b: Vx V — » F which satisfies 1 ) b(av, + B v-, ; v ) = ab...
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Differentiable Manifolds

Lawrence Conlon - 2008 - 418 pages
...this identifies the monomial e^ej^ • • • e*ik with (e^ei, • • • eik)* . Definition 7.3.6. Let V be a finite dimensional vector space over a field F of characteristic zero. A function / : V — > ¥ is a homogeneous polynomial of degree k on V if, relative...
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Spherical Inversion on SLn

Jay Jorgenson, Serge Lang - 2001 - 426 pages
...y', (cf. Lemma 3.2 below). VII, §2. THE CASIMIR DIFFERENTIAL OPERATOR We start with some multilinear algebra. Let V be a finite dimensional vector space over a field of characteristic ^ 2 (because we are going to use symmetric bilinear forms and quadratic forms and...
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Reflection Groups and Invariant Theory

Richard Kane - 2001 - 379 pages
...pseudo-reflection. As we shall see in §14-3, this is only a true generalization for the "modular case". Let V be a finite dimensional vector space over a field F. Definition: A pseudo-reflection is a linear isomorphism s: V — > V that is not the identity map,...
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A First Graduate Course in Abstract Algebra

W.J. Wickless - 2004 - 250 pages
...Show that the simple Z-modules are just the cyclic groups of the form Z(p) for pa prime. Problem 6.2.2 Let V be a finite dimensional vector space over a field F and let R = Lp(V) be the ring of linear transformations from V to V. Prove that V is a simple R-module....
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