A Concise Introduction to Linear Algebra (PDF)

This book offers a refreshingly concise, manageable introduction to linear algebra: Whereas most treatments of the subject give an exhaustive survey supplemented with applications, this book presents a carefully selected array of the most essential topics that can be thoroughly covered in a single semester.

The exposition generally falls in line with the material recommended by the Linear Algebra Curriculum Study Group, but notably deviates in providing an early emphasis on the geometric foundations of linear algebra.  Starting with vectors, lines, and planes in two and three dimensions gives students a more intuitive understanding of the subject and enables an easier grasp of more abstract concepts.  Two important pedagogical devices are also directed to this end: First, throughout the book, the notation is carefully selected to indicate the connections between related quantities; second, in addition to numbering, brief mnemonic titles are appended to theorems and examples, making it easier for the student to internalize and recall important concepts (e.g., it is much more satisfying to recall the Dimension Theorem than to recall Theorem 3.5.1).

The focus throughout is primarily on fundamentals, guiding readers to appreciate the elegance and interconnectedness of linear algebra.  At the same time, the text presents a number of interesting, targeted applications, offering a glimpse of how the subject is used in other fields, especially in physics.  A section on computer graphics and a chapter on numerical methods also provide looks at the potential uses of linear algebra, and most sections contain exercises using MATLAB^® to put theory into practice in a variety of contexts.  Visuals and problems are included to enhance and reinforce understanding throughout the book, and both students' and instructors' solutions manuals (for non-MATLAB exercises) are available online.

A Concise Introduction toLinear Algebra builds on the author's previous title on the subject (Introduction to Linear Algebra, Jones & Bartlett, 1996).  With brevity, precision, and rigor, the work is an ideal choice for a standard one-semester course targeted primarily at math or physics majors.  It is a valuable addition to the book collection of anyone who teaches or studies the subject.