A Bridge to linear algebra/ Dragu Atanasiu, Piotr Mikusinski

Includes bibliographical references & index

Preface -- 1. Basic ideas of linear algebra -- 2. Matrices -- 3. The Vector space R square -- 4. The Vector space R cube -- 5. Determinants and bases in R cube -- 6. Singular value decomposition of 3x2 matrices -- 7. Diagonalization of 3 x 3 matrices -- 8. Applications to geometry -- 9. Rotations -- 10. Problems in plane geometry -- 11. Problems for a computer algebra system -- 12. Answers to selected exercises

The book makes a first course in linear algebra more accessible to the majority of students and it assumes no prior knowledge of the subject. It provides a careful presentation of particular cases of all core topics. Students will find that the explanations are clear and detailed in manner. It is considered as a bridge over the obstacles in linear algebra and can be used with or without the help of an instructor. While many linear algebra texts neglect geometry, this book includes numerous geometrical applications. For example, the book presents classical analytic geometry using concepts and methods from linear algebra, discusses rotations from a geometric viewpoint, gives a rigorous interpretation of the right-hand rule for the cross product using rotations and applies linear algebra to solve some nontrivial plane geometry problems. Many students studying mathematics, physics, engineering and economics find learning introductory linear algebra difficult as it has high elements of abstraction that are not easy to grasp. This book will come in handy to facilitate the understanding of linear algebra whereby it gives a comprehensive, concrete treatment of linear algebra in R² and R³. This method has been shown to improve, sometimes dramatically, a student's view of the subject.