[HPsquared]

In this case can people just prepend "hyper-" as in hyperplane etc? Hyper-line, hyper-angle. (Speaking as someone who has heard 'hyperplane' a few times but not others)

[klodolph]

No, that would be incorrect. A plane is 2D. If you have two functions, and take their span, you get a 2D plane. It is a regular, flat, 2D plane.

When people say “hyperplane” they are generally talking about something with more than two dimensions.

[drdeca]

At least when the ambient vector space is more than 3-dimensional, yeah. Specifically, a hyperplane generally refers to something with codimension 1.

(So, when the ambient vector space is finite-dimensional, the dimension of a hyperplane is one less than the dimension of the ambient vector space.)