Details about A Concise Introduction to Linear Algebra
A Concise Introduction to Linear Algebra PDF free download – This book is designed for a one-semester, post-calculus linear algebra course, primarily intended for mathematics, physics, and computer science majors. While basic calculus is a prerequisite for such a course, very little of it is used in the book. Certainly, multivariable calculus is not required. Vectors are treated fully in Chapter 1, but for classes familiar with them, this chapter may be skipped or just reviewed briefly.
Complex numbers, series, and exponentials are presented briefly in an appendix, but they are needed only in Section 7.4, which may not be covered in some courses. The selection of topics conforms to a large extent to the recommendations of the Linear Algebra Curriculum Study Group.1 The main differences are that the book begins with a chapter on Euclidean vector geometry, mostly in three dimensions; determinants are treated more fully and are placed just before eigenvalues, which is where they are needed; the LU factorization is relegated to Chapter 8 on numerical methods; and the facts about linear transformations are collected in one chapter and are treated in more detail.
This book is considerably shorter than the 400 to 800 pages of most introductory linear algebra books, which are more suitable for two- or threesemester courses. While many applications are presented, they are mostly taken from physics, and several new ones have been added in the second edition. However, these examples give only a glimpse of how the subject is used in other fields, and further details are left to texts in those fields. There is, though, a section on computer graphics and a chapter on numerical methods. Also, most sections contain MATLAB exercises. On the other hand, we hope that the student’s interest will be aroused not only by the possible applications, but also by the geometrical background and the beautiful structure of linear algebra. Nevertheless, for readers especially interested in applications, a list of the ones discussed follows this preface.