query: Prove that any element of vector space $V \otimes W$ can be represented as $\sum \limits_{i=0}^{r}v_i \otimes w_i$
positive_passages.docid: 106047
positive_passages.text: Does every element of tensor product look like this?
negative_passages.docid: 34272
negative_passages.text: Proving definition of norms induced by vector norms
negative_passages.docid: 145447
negative_passages.text: bilinear form - proof
negative_passages.docid: 147450
negative_passages.text: Prove that every bilinear map can be written as a sum of bilinear symmetric map and a bilinear anti-symmetric map.
negative_passages.docid: 95513
negative_passages.text: Proving $W$ is a subspace of $P_{2}$
negative_passages.docid: 62065
negative_passages.text: Prove that $v_1, \dots v_n$ is a basis of V.
negative_passages.docid: 86497
negative_passages.text: Prove that any rational can be expressed in the form $\sum\limits_{k=1}^n{\frac{1}{a_k}}$, $a_k\in\mathbb N^*$
negative_passages.docid: 16692
negative_passages.text: a representation condition of Hilbert space
negative_passages.docid: 14576
negative_passages.text: $(U\cap W)^0 = U^0 + W^0$
negative_passages.docid: 61038
negative_passages.text: Understanding the Details of the Construction of the Tensor Product
negative_passages.docid: 131993
negative_passages.text: Prove that vector space and dual space have same dimension
negative_passages.docid: 74623
negative_passages.text: Associative rule of subspaces and vector spaces: $(U+V) \cap W = U + (V \cap W)$
negative_passages.docid: 82464
negative_passages.text: $U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces
negative_passages.docid: 121636
negative_passages.text: General linear group of a vector space
negative_passages.docid: 43987
negative_passages.text: Decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields
negative_passages.docid: 116823
negative_passages.text: VERIFYING: Proving an $n \times n$ Matrix Vector Space
negative_passages.docid: 69474
negative_passages.text: Orthogonal projections with $\sum P_i =I$, proving that $i\ne j \Rightarrow  P_{j}P_{i}=0$