or Cartesian space, n. 1. a finite-dimensional real or complex vector space possessing a scalar product, so that a Euclidean distance may be imposed. Most commonly, one begins with the n-fold Cartesian product of the real or complex fields. This represents the most common and useful abstraction and extension of the mathematical representation of the three-dimensional space of daily experience in terms of Cartesian coordinates, and is referred to as Euclidean n-space, where n is the dimension of the space. 2. less commonly, any finite or infinite inner product space.