A frame of reference is a system of coordinates used to described the position of an object in some space. The space is typically assumed to be "real space", . A frame of reference possesses an origin, a special point used as a reference for all other points, and a set of axes, which represent the possible directions in which an object can move.
Mathematically, a frame of reference is the choice of a Basis within a Vector space, alongside the choice of a point of origin in that space. The most common frame of reference is Cartesian coordinates in with set as the origin.
A frame of reference is said to be inertial if Newton's first law holds within the frame and noninertial otherwise. In practice, the frame is inertial if the origin is at rest of it is moving at a constant velocity.