Prove that $\nabla \times (\nabla \times \vec A) = \nabla(\nabla \cdot \vec A) - \nabla^2\vec A$. For any vector function of $\vec A$.
103308
Showing that $\nabla\times(\nabla\times\vec{A}) = \nabla(\nabla\cdot\vec{A})-\Delta\vec{A}$
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
4240
The proof of Triple Vector Products
110654
Vector Spaces and AC
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
11259
Prove $R\times S$ is not an integral domain
77951
Dirac's delta in 3 dimensions: proof of $\nabla^2(\|\boldsymbol{x}-\boldsymbol{x}_0\|^{-1})=-4\pi\delta(\boldsymbol{x}-\boldsymbol{x}_0)$
111348
Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$
3433
Proof if $a \vec v = 0$ then $a = 0$ or $\vec v = 0$
100608
Prove that $\|v\|_{H^1(\Omega )}\leq C(\|f\|_{L^2(\Omega )}+\|v\|_{H^{1/2}(\partial \Omega )}+\|\partial _\nu v\|_{H^{1/2}(\partial \Omega )}))$
145173
$f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$
95379
Prove that $V = V_1 \oplus V_2$ in the following
52973
The identity $(u\times v)\cdot(x\times y)=\begin{vmatrix}u\cdot x&v\cdot x\\ u\cdot y&v\cdot y\\\end{vmatrix}$
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
38428
How tot start proving $A \times B \times C \ne (A \times B) \times C$?
119579
$S^2 \times S^2$ is diffeomophic to $G_2(\mathbb{R}^4)$
133087
Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.