How to show that $\sum_{i=1}^n|\lambda_i|\leq \sum_{i,j}|a_{ij}|$?
73952
Upper bound for the sum of absolute values of the eigenvalues
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
119317
Proving the series of partial sums of $\sin (in)$ is bounded?
154085
$\sum a_i \ln(b_i) \leq \sum a_i \ln(a_i)$ with $\sum a_i = \sum b_i = 1$
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
155005
How to show $\sum_{k=n}^\infty{\frac{1}{k!}} \leq \frac{2}{n!}$
54900
How to prove $|\sum_{i=1}^n a_i|\le \sqrt{n} \sqrt{\sum_{i=1}^n a_i^2}$
73406
Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
106609
Show that $e^{iy} = 1 + iy + \frac{\mu_1 y^2}{2}$ for all $y \in \mathbb{R}$ with $|\mu_1| \leq 1$
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
118613
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
132541
Showing ${1\over n}\sum|S_i|=O(\sqrt n)$ for $S_i\subset [n]$, $|S_i\cap S_i|\le 1$ for $i\ne j$
153448
Show that $A\in\mathbb{C}_n$ is normal $\iff$ $tr(A*A) = \sum_{i = 1}^n|\lambda_i|^2$, where $\lambda_1,...,\lambda_n$ are the eigenvalues of $A$.
63124
Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
7457
Prove that $J^+AJ$ has positive eigenvalues
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
67820
Showing that $(A_{ij})=\left(\frac1{1+x_i+x_j}\right)$ is positive semidefinite