Need help proving $\langle u,v\rangle = 0$ iff $ \|u\| \le \|u+cv\|$ for all scalars $c$.
34147
$\|u\|\leq \|u+av\| \Longrightarrow \langle u,v\rangle=0$
94077
Proof of linear independence of $e^{at}$
48563
If $\Gamma^k_{ij}(p)=0$, then $\nabla_{E_i}E_j (p)=0?$
9003
prove $\frac{1}{2}\mathbf{\nabla (u \cdot u) = u \times (\nabla \times u ) + (u \cdot \nabla)u}$ using index notation
100608
Prove that $\|v\|_{H^1(\Omega )}\leq C(\|f\|_{L^2(\Omega )}+\|v\|_{H^{1/2}(\partial \Omega )}+\|\partial _\nu v\|_{H^{1/2}(\partial \Omega )}))$
31919
What can we say about the inner product $\langle f(t),f'(t) \rangle$?
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
50428
Proof of Neumann Lemma
81879
$Av=λv$ basis proof problems
46669
How can I prove these are the adjoint operators?
45682
Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$
121802
Prove that every self-adjoint unitary linear operator can be expressed in the form $U\alpha = \beta - \gamma$
109228
Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent
76110
Proving that the zero vector is unique
73406
Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
100810
Let $V$ be spherically symmetric and $W$ i.i.d. Gaussian. Then $E[V|V+W=t]=g(\|t\|)$
71187
How to prove $\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle$,using $[\hat{x},\hat{p}]=i\hbar$?