# Tagged Questions

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### Pointed Convex cone: one-to-one correspondence extreme rays - extreme points

Hoi, let $V$ be a finite dimensional real vector space with inner product $\left\langle .\right\rangle$. Let $\Gamma\subset V$ and $\Gamma \neq \left\{0\right\}$ a pointed convex cone. (Pointed means ...
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### Projection operator property

Let $\pi_M(a)$(projection operator) be the closest point of $M$ from the point $a$ . How one can prove if $M$ is convex set of $\mathbb R^n$ then projection operator has this property? ...
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### Definition of direct products of two cones or of two convex subsets?

When reading a comment after this reply, I was wondering what the definitions of direct product of two cones? More generally, what is the direct product of two convex subsets? This case is what I ...
Prove that the function $f:\mathbb{R}^n\to \mathbb{R}$ given by $f(x)=x^T \cdot x$ is strictly convex. Use this result to find the absolute minimum by equating the derivative to zero. I am not sure ...