query: Is $\nabla \cdot (\nabla\times \textbf{F})$ = div $\textbf{F} $?
positive_passages.docid: 27467
positive_passages.text: What is an intuitive explanation for $\operatorname{div} \operatorname{curl} F = 0$?
negative_passages.docid: 75604
negative_passages.text: Proof that $\partial(A\times B) = ((\partial A)\times B)\cup (A\times(\partial B))$
negative_passages.docid: 107389
negative_passages.text: Show that the vector space of real functions is not finitely spanned
negative_passages.docid: 98800
negative_passages.text: Do local flows of left-invariant vector fields satisfy $\Phi_X^t\circ L_x=L_x\circ \Phi_X^t$?
negative_passages.docid: 103061
negative_passages.text: Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
negative_passages.docid: 71767
negative_passages.text: What is the difference between $\Bbb{R^n}\times\Bbb{R^m}$ and $\Bbb{R^{m+n}}$?
negative_passages.docid: 25397
negative_passages.text: Prove $R \times R$ is NOT an integral domain
negative_passages.docid: 56936
negative_passages.text: $\frac{\partial f_i}{x_j}=\frac{\partial f_j}{x_i}\implies(f_1,\ldots,f_n)$ is a gradient
negative_passages.docid: 28500
negative_passages.text: What are the components and path components of $\mathbb{R}^{\omega}$ in the product, uniform, and box topologies?
negative_passages.docid: 97391
negative_passages.text: Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space
negative_passages.docid: 61144
negative_passages.text: Derivative of $x^{x^{\cdot^{\cdot}}}$?
negative_passages.docid: 21553
negative_passages.text: Prove that $\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$
negative_passages.docid: 29030
negative_passages.text: Vector space with new scalar multiplication defined over finite field still vector space?
negative_passages.docid: 55393
negative_passages.text: Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
negative_passages.docid: 95976
negative_passages.text: Given a PRF $F$ , is $G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$ a PRG?
negative_passages.docid: 151117
negative_passages.text: Are all fields vector spaces?
negative_passages.docid: 24585
negative_passages.text: Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$