共查询到20条相似文献,搜索用时 0 毫秒
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Let V be a 6-dimensional vector space over a field , let f be a nondegenerate alternating bilinear form on V and let denote the symplectic group associated with . The group has a natural action on the third exterior power of V and this action defines five families of nonzero trivectors of V. Four of these families are orbits for any choice of the field . The orbits of the fifth family are in one-to-one correspondence with the quadratic extensions of that are contained in a fixed algebraic closure of . In this paper, we divide the orbits corresponding to the separable quadratic extensions into suborbits for the action of on . 相似文献
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Hisatoshi Ikai 《Linear algebra and its applications》2011,434(4):1094-1106
Based on the relation of exponential maps and interior products in exterior algebras, some formulas of Pfaffians, including expansion formulas and the Cayley-Jacobi formula for determinants of alternating matrices, are deduced with new proofs. As an application, Pfaffian powers of alternating bilinear forms [O. Loos, Discriminant algebras and adjoints of quadratic forms, Beiträge Algebra Geom. 38 (1997) 33-72] are interpreted in terms of exponential maps in algebras of alternating multi-linear forms. 相似文献
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Let V be a vector space over a field or skew field F, and let U be its subspace. We study the canonical form problem for bilinear or sesquilinear forms
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We present a theory of the definiteness (nonnegativity and positivity) of a quadratic functional F over a bounded time scale. The results are given in terms of a time scale symplectic system (S), which is a time scale linear system that generalizes and unifies the linear Hamiltonian differential system and discrete symplectic system. The novelty of this paper resides in removing the assumption of normality in the characterization of the positivity of F, and in establishing equivalent conditions for the nonnegativity of F without any normality assumption. To reach this goal, a new notion of generalized focal points for conjoined bases (X,U) of (S) is introduced, results on the piecewise-constant kernel of X(t) are obtained, and various Picone-type identities are derived under the piecewise-constant kernel condition. The results of this paper generalize and unify recent ones in each of the discrete and continuous time setting, and constitute a keystone for further development in this theory. 相似文献
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Bart De Bruyn 《Linear algebra and its applications》2011,435(5):1055-1084
We investigate relationships between polyvectors of a vector space V, alternating multilinear forms on V, hyperplanes of projective Grassmannians and regular spreads of projective spaces. Suppose V is an n-dimensional vector space over a field F and that An-1,k(F) is the Grassmannian of the (k − 1)-dimensional subspaces of PG(V) (1 ? k ? n − 1). With each hyperplane H of An-1,k(F), we associate an (n − k)-vector of V (i.e., a vector of ∧n−kV) which we will call a representative vector of H. One of the problems which we consider is the isomorphism problem of hyperplanes of An-1,k(F), i.e., how isomorphism of hyperplanes can be recognized in terms of their representative vectors. Special attention is paid here to the case n = 2k and to those isomorphisms which arise from dualities of PG(V). We also prove that with each regular spread of the projective space PG(2k-1,F), there is associated some class of isomorphic hyperplanes of the Grassmannian A2k-1,k(F), and we study some properties of these hyperplanes. The above investigations allow us to obtain a new proof for the classification, up to equivalence, of the trivectors of a 6-dimensional vector space over an arbitrary field F, and to obtain a classification, up to isomorphism, of all hyperplanes of A5,3(F). 相似文献
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Let α be a rational-valued set-function on then-element sexX i.e. α(B) εQ for everyB ⫅X. We say that α defines a 0-configuration with respect toA⫅2
x
if for everyA εA we have
α(B)=0. The 0-configurations form a vector space of dimension 2
n
− |A| (Theorem 1). Let 0 ≦t<k ≦n and letA={A ⫅X: |A| ≦t}. We show that in this case the 0-configurations satisfying α(B)=0 for |B|>k form a vector space of dimension
, we exhibit a basis for this space (Theorem 4). Also a result of Frankl, Wilson [3] is strengthened (Theorem 6). 相似文献
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Stéphane Jaffard Marius Tucsnak Enrique Zuazua 《Journal of Fourier Analysis and Applications》1997,3(5):577-582
We prove a trigonometric inequality of Ingham’s type for nonharmonic Fourier series when the gap condition between frequencies
does not hold any more.
Partially supported by grants PB93-1203 of the DGICYT (Spain) and CHRX-CT94-04771 of the UE. 相似文献
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If E is a vector space over a field K, then any regular symmetric bilinear form on E induces a polarity
on the lattice of all subspaces of E. In the particular case where E is 3-dimensional, the set of all subspaces M of E such that both M and
are not N-subspaces (which, in most cases, is equivalent to saying that M is nonisotropic), ordered by inclusion and endowed with the restriction of the above polarity, is an orthomodular lattice T(E, ). We show that if K is a proper subfield of K, with K F2, and E a 3-dimensional K -subspace of E such that the restriction of to E × E is, up to multiplicative constant, a bilinear form on the K -space E , then T(E , ) is isomorphic to an irreducible 3-homogeneous proper subalgebra of T(E, ). Our main result is a structure theorem stating that, when K is not of characteristic 3, the converse is true, i.e., any irreducible 3-homogeneous proper subalgebra of T(E, ) is of this form. As a corollary, we construct infinitely many finite orthomodular lattices which are minimal in the sense that all their proper subalgebras are modular. In fact, this last result was our initial aim in this paper.Received June 4, 2003; accepted in final form May 18, 2004. 相似文献
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Summary We prove that graphs of continuous maps with finite area can be approximated weakly as currents and in area by graphs of smooth maps.This article was processed by the author using the style filepljour1m from Springer-Verlag. 相似文献
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Dragomir Ž. Djoković 《Linear and Multilinear Algebra》2013,61(1):3-39
Let U?V denote the tensor product of two finite dimensional vector spaces U and V over an infinite field. Let k be a positive integer such that kdim U and k dim V Let Dk denote the set of all non-zero elements of U?V of rank less than k. In this paper we study linear transformations T on U?V such that (TDk )?Dk . 相似文献
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Mihai Halic 《manuscripta mathematica》1999,99(3):371-381
The article investigates the geography of closed, connected and simply connected, six-dimensional manifolds. It is proved
that any triple of integers satisfying some necessary arithmetical restrictions occurs as the Chern triple of such a manifold.
The main tools used for producing the examples are the symplectic connected sum and the symplectic blow-up.
Received: 28 May 1998 / Revised version: 22 January 1999 相似文献
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We classify all (finitely dimensional) nilpotent Lie k-algebras h with 2-dimensional commutator ideals h′, extending a known result to the case where h′ is non-central and k is an arbitrary field. It turns out that, while the structure of h depends on the field k if h′ is central, it is independent of k if h′ is non-central and is uniquely determined by the dimension of h. In the case where k is algebraically or real closed, we also list all nilpotent Lie k-algebras h with 2-dimensional central commutator ideals h′ and dimkh?11. 相似文献
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Steven H. Weintraub 《Journal of Geometry》2007,86(1-2):165-180
Let V be a vector space of dimension 2n, n even, over a field F, equipped with a nonsingular symplectic form. We define a new algebraic/combinatorial structure, a spread of nonsingular
pairs, or nsp-spread, on V and show that nsp-spreads exist in considerable generality. We further examine in detail some particular cases. 相似文献
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A. Kulesko 《Integral Equations and Operator Theory》1996,25(1):94-103
The spectrum and the Jordan structure of a matrix pencilA
z
=z
–1
B+C+zB
T
has been considered. The results have been applied to investigation of the spectrum of two-side infinite periodic Jacobi matrices. 相似文献