Multilinear forms
نویسنده
چکیده
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 ) as follows. If v ∈ V , then we define ψ(v) to be the element of V ∗ given by
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