ABSTRACT
This chapter describes some basic properties of vector spaces. There are numerous examples of structures that form vector spaces. The chapter provides a few examples of such structures. The examples indicate that matrices and polynomials can also be used to form vector spaces over any field. The chapter discusses linearly independent and linearly dependent vectors, which are sets of vectors that span a vector space, bases, and the dimension of a vector space. It considers subsets of vector spaces, which themselves form vector spaces. There are numerous examples of structures that form subspaces of various vector spaces. The chapter also provides several examples of subspaces involving various kinds of matrices.
