ABSTRACT
The fact that finite-dimensional vector (or linear) spaces are the fundamental setting of matrix theory is probably known to the reader. On the other hand, it is also true that-by simply considering a matrix as an array of numbersmany aspects of matrix theory and manipulation can be examined without ever even mentioning the notion of linear space. In the writer’s opinion, this kind of approach tends to conceal the important interplay between matrices and linear transformations (or operators) defined on vector spaces-typically
n or n-in which a matrix is just a particular representation of a linear transformation and different matrices may represent the same linear operator. It is in this light that we approach the subject by giving some basic concepts and definitions of finite-dimensional vector spaces.
