# Characterisation of linearly separable points of a hypercube

Essentially, linearly separable points are just those corners that can be cut off with just one slice as marked out by a hyperplane.

E.g. for a cube, the following 4 points (red) are not linearly separable - no single cut by a plane (tilted at whatever angle) across the cube can slice off exactly these 4 points:

So this begs the question: given $n$ points on an $m$-dimensional hypercube, how can I tell if these $n$ points are linearly separable?

• @AsalBeagDubh - thanks, sounds like that might be what I want, but what is $p_i - p_0$? Jun 5, 2013 at 15:40
• Sorry, I deleted my comment because I think I misread the question. $p_i-p_0$ just means the vector pointing from the point $p_0$ to the point $p_i$.
– user64687
Jun 5, 2013 at 17:03
• Jun 9, 2013 at 18:34