If $\|u\| \leq \|u+av\|$ for all $a \in F$, How can I show that $\langle u,v\rangle=0$?
34147
$\|u\|\leq \|u+av\| \Longrightarrow \langle u,v\rangle=0$
48498
Fourier coefficients $\langle x,e_k\rangle$ are at countable
76790
Condition to guarantee $f=0$ on $[a,b]$
34702
Show $|A + uv^T| = (1 + v^T A^{-1} u) |A|$
149287
Prove that $A,B>0$ and $A_{ij}0$
128710
Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
63124
Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
71187
How to prove $\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle$,using $[\hat{x},\hat{p}]=i\hbar$?
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
102990
Prove or disprove: $S_{10} = \langle (1,3),(1,2, ... ,10) \rangle$
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
7813
In a complex vector space, $\langle Tx,x \rangle=0 \implies T = 0$
55461
How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
45682
Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$
42334
Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?