“tensor product”的概念、定义、习题解题方法及翻译-数学辞典

单词

tensor product

释义

tensor product

Given vector spaces V and W (over the same field F), with bases v1,…,vm and w1,…,wn respectively, the tensor product V ⊗ W may be defined as the vector space spanned by the formal symbols vi ⊗ wj. 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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数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。