“tensor product”的概念、定义、翻译、参考文献-科学参考

tensor product

Mathematics

Given vector spaces V and W (over the same field F), with bases v₁,…,v_m and w₁,…,w_n respectively, the tensor product V ⊗ W may be defined as the vector space spanned by the formal symbols v_i ⊗ w_j. This then defines a vector space of dimension mn.
More naturally, V ⊗ W may be defined without reference to bases, as the dual space of the space of bilinear maps B: V × W → F via (v ⊗ w)(B) = B(v,w). Further, Hom(V,W) is then isomorphic to V* ⊗ W via (f ⊗ w)(v) = f(v)w.

单词	tensor product
释义	tensor product Mathematics Given vector spaces V and W (over the same field F), with bases v₁,…,v_m and w₁,…,w_n respectively, the tensor product V ⊗ W may be defined as the vector space spanned by the formal symbols v_i ⊗ w_j. This then defines a vector space of dimension mn. More naturally, V ⊗ W may be defined without reference to bases, as the dual space of the space of bilinear maps B: V × W → F via (v ⊗ w)(B) = B(v,w). Further, Hom(V,W) is then isomorphic to V* ⊗ W via (f ⊗ w)(v) = f(v)w.
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