James type results for polynomials and 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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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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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 2004
ISSN: 0004-2080
DOI: 10.1007/bf02432907