ABSTRACT
A major goal of abstract algebra is the classification of algebraic structures. An example of such a classification is the theorem of linear algebra stating that every finite-dimensional real vector space V is isomorphic to Rn for some natural number n. Moreover, the number n is uniquely determined by V and is the dimension of V as a vector space. This classification theorem is useful because, in principle, we can use it to reduce the study of abstract vector spaces such as V to the concrete, familiar vector spaces Rn.
