The definition of a "vector" in physics (including both polar vectors and pseudovectors) is more specific than the mathematical definition of "vector" (namely, any element of an abstract vector space). Under the physics definition, a "vector" is required to have components that "transform" in a certain way under a proper rotation: In particular, if everything in the universe were rotated, the vector would rotate in exactly the same way. (The coordinate system is fixed in this discussion; in other words this is the perspective of active transformations.) Mathematically, if everything in the universe undergoes a rotation described by a rotation matrix "R", so that a displacement vector x is transformed to , then any "vector" v must be similarly transformed to . This important requirement is what distinguishes a "vector" (which might be composed of, for example, the "x"-, "y"-, and "z"-components of velocity) from any other triplet of physical quantities (For example, the length, width, and height of a rectangular box "cannot" be considered the three components of a vector, since rotating the box does not appropriately transform these three components.)