Fundamentals of Linear Algebra

Linear algebra has evolved as a branch of mathematics with wide range of applications to the natural sciences, to engineering, to computer sciences, to management and social sciences, and more.

This book is addressed primarily to second and third year college students who have already had a course in calculus and analytic geometry. It is the result of lecture notes given by the author at The University of North Texas and the University of Texas at Austin. It has been designed for use either as a supplement of standard textbooks or as a textbook for a formal course in linear algebra.

This book is not a "traditional" book in the sense that it does not include any applications to the material discussed. Its aim is solely to learn the basic theory of linear algebra within a semester period. Instructors may wish to incorporate material from various fields of applications into a course.

I have included as many problems as possible of varying degrees of diffculty. Most of the exercises are computational, others are routine and seek to fix some ideas in the reader's mind; yet others are of theoretical nature and have the intention to enhance the reader's mathematical reasoning. After all doing mathematics is the way to learn mathematics.