Vectors and Vector Spaces

Vector spaces are mathematical structures consisting of collections of vectors together with operations on those vectors. The elements of the vectors must themselves be members of fields, which are mathematical structures consisting of sets and two operations (usually called addition and multiplication) defined on those sets. The two most common and familiar fields are the field of real numbers and the field of complex numbers. The field of real numbers is denoted by \(\mathbb {R}\) and is just called the reals.