Prove that $\langle x,y \rangle = 0$ iff $\|x+cy\| \geq \|x\|$ for all real $c$.
72920
$x \perp y$ if and only if $\Vert x + \alpha y \Vert \ge \Vert x \Vert$ for all scalars $\alpha$
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
45555
$(x+y)^c\le x^c+y^c$ for $0<c\le1$
57166
Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
128932
Is my expansion of the state $| x \rangle$ correct?
14759
Prove that $ f(z) = 0 $ for all $ z \in \overline{D}(0,1) $.
91627
What is a primary decomposition of the ideal $I = \langle xy, x - yz \rangle$?
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
103870
$3.\lim_{n\to\infty}\langle x,e_n\rangle=?$
83050
Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
30569
Prove that the only operator on $\mathbb{C}$ for which his inner product is zero is zero
155864
Prove or disprove: if $y'=y-y^2$ and $y(0)=a$ where $00$
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
120766
Prove ${y_n}$ is a basis for a Hilbert space $H$.
16948
Need help with a proof that if $xy=0$ then $x=0$ or $y=0$
71187
How to prove $\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle$,using $[\hat{x},\hat{p}]=i\hbar$?