Prove that the norm of $E$ is generate by the inner product $\langle x,y \rangle =\frac{1}{4}\left(||x+y|^2-||x-y||^2\right)$
57619
Norms Induced by Inner Products and the Parallelogram Law
82729
Prove that $\mathrm E\left({\max}\left\{X^2 , Y^2\right\} \right) \leq 1 + \sqrt{1 - \rho^2}$ where $\rho$ is their correlation.
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
51276
Prove that in Bell's inequality $\langle{\Psi}|\left(\bf{\sigma}\cdot\bf{a}\right)\left(\bf{\sigma}\cdot\bf{b}\right)|{\Psi}\rangle=-\bf a \cdot\bf b$
143869
Showing that the norm of the canonical projection $X\to X/M$ is $1$
99024
Let $\,E=\{(x,y) \in \Bbb R^2: |x| \le 1,|y|\le 1\}.$
155317
Norm of adjoint operator in Hilbert space
27086
proof for $\langle q| p \rangle = e^{ipq}$
70415
Comparison between the $\ell_1$ and $\ell_2$ norms
109295
Proving $1-\exp(-4x^2/ \pi) \ge \text{erf}(x)^2$
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
89089
Prove that there is a unique inner product on $V$
77752
Show that $e^{x+y}=e^xe^y$ using $e^x=\lim_{n\to\infty }\left(1+\frac{x}{n}\right)^n$.
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
149362
Prove that $ \mathbb{E}[XY] - \mathbb{E}[X] \mathbb{E}[Y] = \int_{- \infty}^\infty \int_{- \infty}^\infty (F(x,y)-F_X(x) F_Y(y)) \,dx\,dy,$
44685
Inner product on $C(\mathbb R)$
113411
If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?