Introduction to Linear Algebra (IE-Paperback)

Gilbert Strang




I will be happy with this preface if three important points come through clearly :
1. The beauty and variety of linear algebra, and its extreme usefulness
2. The goals of this book, and the new features in this International Edition
3. The steady support from our linear algebra websites and the video lectures
May I begin with notes about two websites that are constantly used. Messages come from thousands of students and faculty about linear algebra on MIT's OpenCourseWare site. The Math 18.06 course includes video lectures of a complete semester of classes and 18.06SC adds problem solutions by MIT teachers. The video lectures offer an independent review of the whole subject based on this book. Ten million viewers around the world have seen these videos (amazing). I hope you find them helpful. This website is a permanent record of ideas and good problems. Solutions are now included for this International Edition. Several sections of the book are directly available online, plus notes on teaching linear algebra. The content is growing quickly and contributions are welcome from everyone.


Gilbert Strang is a professor of mathematics at the Massachusetts Institute of Technology, where his research focuses on analysis, linear algebra and PDEs. He is the author of many textbooks and his service to the mathematics community is extensive. He has spent time both as President of SIAM and as Chair of the Joint Policy Board for Mathematics, and has been a member of various other committees and boards. He has received several awards for his research and teaching, including the Chauvenet Prize (1976), the Award for Distinguished Service (SIAM, 2003), the Graduate School Teaching Award (Massachusetts Institute of Technology, 2003) and the Von Neumann Prize Medal (US Association for Computational Mechanics, 2005), among others. He is a Member of the National Academy of Sciences, a Fellow of the American Academy of Arts and Sciences, and an Honorary Fellow of Balliol College, Oxford.


1. Introduction to vectors
2. Solving linear equations
3. Vector spaces and subspaces
4. Orthogonality
5. Determinants
6. Eigenvalues and eigenvectors
7. Linear transformations
8. Applications
9. Numerical linear algebra
10. Complex vectors and matrices