query: The proof of Triple Vector Products
positive_passages.docid: 21807
positive_passages.text: on proving bac-cab rule, $\vec{A} \times ( \vec{B} \times \vec{C})= \vec{B} (\vec{A} \cdot\vec{C})- \vec{C}(\vec{A}\cdot\vec{B})$
negative_passages.docid: 39585
negative_passages.text: Connection between rank and matrix product
negative_passages.docid: 104258
negative_passages.text: Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
negative_passages.docid: 85193
negative_passages.text: direct product commutes with tensor product?
negative_passages.docid: 25553
negative_passages.text: elementary set theory (cartesian product and symmetric difference proof)
negative_passages.docid: 103106
negative_passages.text: Proving that any permutation in $S_n$ can be written as a product of disjoint cycles
negative_passages.docid: 102383
negative_passages.text: Associativity of Cartesian Product
negative_passages.docid: 15560
negative_passages.text: Prove that the union of three subspaces of $V$ is a subspace iff one of the subspaces contains the other two.
negative_passages.docid: 62123
negative_passages.text: Proving that Tensor Product is Associative
negative_passages.docid: 31631
negative_passages.text: Proof Verification: Joint variance of the product of a random matrix with a random vector
negative_passages.docid: 81879
negative_passages.text: $Av=λv$ basis proof problems
negative_passages.docid: 48524
negative_passages.text: Existence proof of the tensor product using the Adjoint functor theorem.
negative_passages.docid: 41520
negative_passages.text: Prove that $L(V,W)$ forms a vector space
negative_passages.docid: 89089
negative_passages.text: Prove that there is a unique inner product on $V$
negative_passages.docid: 8970
negative_passages.text: Proving the cross product matrix tranformation identity with an alternative solution
negative_passages.docid: 145447
negative_passages.text: bilinear form - proof
negative_passages.docid: 54737
negative_passages.text: Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$