When the scalar field is the real numbers , the vector space is called a "real vector space". When the scalar field is the complex numbers , the vector space is called a "complex vector space". These two cases are the ones used most often in engineering. The general definition of a vector space allows scalars to be elements of any fixed field . The notion is then known as an -"vector space" or a "vector space over ". A field is, essentially, a set of numbers possessing addition, subtraction, multiplication and division operations. For example, rational numbers form a field.