The set of m × n matrices, say with real entries, is an example of a mathematical structure with two operations, akin to addition and scalar multiplication of matrices, which satisfy the same basic properties as the matrix operations do. Such structures are known as vector spaces. Examples of vector spaces and their applications are found in every conceivable area of today’s theoretical and technical disciplines. Because these structures occur in such diverse areas, it makes sense to study vector spaces in abstract without referring to specific entities so that a single theory is available to deal with all of them. Before stating the formal definition of a vector space, we have a brief look at some examples of ...