Algebra I: A Basic Course in Abstract Algebra

Chapter 12

Matrices and Linear Transformations

In this chapter we are going to study a special kind of function that arises very naturally in the study of linear algebra and has many applications in other fields such as physics and engineering.

These functions are called linear transformations. We shall show that there is a close relationship between matrices and linear transformations. In fact every m × n matrix gives rise to a linear transformation and vice versa.

12.1 Introduction to Linear Transformations

This section is devoted mostly to the basic definitions and facts associated with this special kind of function. In this section we are going look at functions from ℝⁿ into ℝ^m.

In other words, we are going look at functions that take elements/points/ ...