Linear Algebra
Subject: Mathematics and Linear Algebra
Author or source: Jim Hefferon
Updated:
Jim Hefferon’s complete 525-page fourth edition of Linear Algebra, with systems, vector spaces, linear maps, determinants, eigenvalues and exercises.
Overview of the complete resource
Source page 1–525
This undergraduate textbook connects computations with proofs. It begins with Gaussian elimination and solution sets, then introduces vector spaces, bases, dimension, linear maps and matrix representations. Later chapters develop determinants, eigenvectors, eigenvalues and further linear transformations. Worked examples and exercises build mathematical reasoning alongside matrix calculations. The author supplies a separate worked-solutions book and video lessons. Try exercises before consulting solutions. The MIT examination linked here is authentic related-subject practice from a different university course; it is not an examination for this textbook or an Indian university paper. This overview describes the book as a whole.
Author preface: reading preview
Source page 3
Preface This book helps students to master the material of a standard US undergraduate first course in Linear Algebra. The material is standard in that the subjects covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. Another standard is the book’s audience: sophomores or juniors, usually with a background of at least one semester of calculus. The help that it gives to students comes from taking a developmental approach — this book’s presentation emphasizes motivation and naturalness, using many examples. The developmental approach is what most recommends this book so I will elaborate. Courses at the beginning of a mathematics program focus less on theory and more on calculating. Later courses ask for mathematical maturity: the ability to follow different types of arguments, a familiarity with the themes that underlie many mathematical investigations such as elementary set and function facts, and a capacity for some independent reading and thinking. Some programs have a separate course devoted to developing maturity but in any case a Linear Algebra course is an ideal spot to work on this transition. It comes early in a program so that progress made here pays offlater but it also comes late enough so that the classroom contains only students who are serious about mathematics. The material is accessible, coherent, and elegant. And, examples are plentiful. Helping readers with their transition requires taking the mathematics seri- ously. All of the results here are proved. On the other hand, we cannot assume that students have already arrived and so in contrast with more advanced texts this book is filled with illustrations of the theory, often quite detailed illustrations. Some texts that assume a not-yet sophisticated reader begin with matrix multiplication and determinants. Then, when vector spaces and linear maps finally appear and definitions and proofs start, the abrupt change brings the