The absolute-value estimate for symmetric multilinear forms
نویسندگان
چکیده
منابع مشابه
Symmetric multilinear forms and polarization of polynomials
We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in n variables. The main tool is combinatorial polarization, and the approach is applicable even when n! is not invertible in the underlying field.
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In this paper we obtain some versions of weak compactness James’ theorem, replacing bounded linear functionals by polynomials and symmetric multilinear forms. Mathematics Subject Classification (1991): 46B10, 46B50, 46G25
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The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.
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Proposition 1.1. α1, . . . , αn forms a basis for V ∗ (called the dual basis). In particular, this shows that V and V ∗ are vector spaces of the same dimension. However, there is no natural way to choose an isomorphism between them, unless we pick some additional structure on V (such as a basis or a nondegenerate bilinear form). On the other hand, we can construct an isomorphism ψ from V to (V ...
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We introduce a novel strategy for constructing symmetric positive definite (SPD) preconditioners for linear systems with symmetric indefinite matrices. The strategy, called absolute value preconditioning, is motivated by the observation that the preconditioned minimal residual method with the inverse of the absolute value of the matrix as a preconditioner converges to the exact solution of the ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1990
ISSN: 0024-3795
DOI: 10.1016/0024-3795(90)90284-j