Let $f(x) = x^\top Q \, x$, where $Q \in \mathbb R^{n×n}$ is NOT symmetric. Show that the Hessian is $H_f (x) = Q + Q^\top$
489
How to take the gradient of the quadratic form?
147420
Equivalent definitions of convexity for $f\in\mathcal C^1(\mathbb R^n)$
63526
Proving that $(\sup_{x\in R}|f'(x)|)^2\leq 4\sup_{x\in R}|f(x)|\cdot\sup_{x\in R}|f''(x)|$.
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
132311
T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$
96022
Symmetry of second derivative - Sufficiency of twice-differentiability
123478
Generalized Poincaré Inequality on H1 proof.
97584
How to prove this property using convexity?
10352
Prove that $x^n$ is a convex function on $(0,\infty)$
26658
A proof for $\nabla |u|^p = p\ \text{sgn}(u)|u|^{p-1}\nabla u$.
27344
Showing connection of cross-ratio and Schwarzian derivative for a holomorphic function $f$.
147888
Show that $M=\bigcap_{\mathfrak{p}\in\operatorname{Spec}(R)}M_\mathfrak{p}=\bigcap_{\mathfrak{m}\in\text{Max}(R)}M_\mathfrak{m}$ for certain $M$.
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
84206
How do I show that if $f$ is entire and $\{\lvert f(z)\rvert < M\}$ is connected for all $M$, then $f$ is a power function?
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
53432
What is the algebraic closure of $\mathbb F_q$?
36099
Show that $\|f\|^{2}$ attains a minimum value on the interior of $B$