Linear Algebra

This chapter is about linear algebra. Linear algebra is central to almost all areas of mathematics. Linear algebra is also used in most sciences and fields of engineering. Thus, it occupies a vital part in the university curriculum. Linear algebra is all about matrices, vector spaces, systems of linear equations, eigenvectors, you name it. It is common that a student of linear algebra can do the computations (e.g., compute the determinant of a matrix, or the eigenvector), but he/she usually does not know the why and the what—the theoretical essence of the subject. This chapter hopefully provides some answers to these questions.