Orthant

In geometry, an orthant[1] or hyperoctant[2] is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions.

In general an orthant in n-dimensions can be considered the intersection of n mutually orthogonal half-spaces.

More specifically, a closed orthant in Rn is a subset defined by constraining each Cartesian coordinate to be nonnegative or nonpositive.

Similarly, an open orthant in Rn is a subset defined by a system of strict inequalities where each εi is +1 or −1.

[3] The nonnegative orthant is the generalization of the first quadrant to n-dimensions and is important in many constrained optimization problems.