Let $a$ be a vector in $\mathbb R^n$, and let $c$ be a real number. Is there a simple characterization of the set $\{x\in\mathbb R^n : (a,x) \geq c\}$ where $(a,x)$ is the inner product $\sum_{i=1}^n a_i x_i$.
Well, I'm sure that characterizations exist - but what are they? I am looking in particular for a "computer-friendly" representation. (I have a bunch of such $a$ and $c$, and I want ultimately to intersect sets of the form above, or to find a set [with a simple representation] containing the intersection but not "too much" else.)
Thank you!