A Bridge to Linear Algebra

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.

Contents:

• Basic Ideas of Linear Algebra
• Matrices
• The Vector Space R²;
• The Vector Space R³;
• Determinants and Bases in R³;
• Singular Value Decomposition of 3 x 2 Matrices
• Diagonalization of 3 x 3 Matrices
• Applications to Geometry
• Rotations
• Problems in Plane Geometry
• Problems for a Computer Algebra System
• Answers to Selected Exercises

Readership: Undergraduate students taking a first course in linear algebra.
Key Features:

• The book makes linear algebra more accessible to the majority of students by giving a concrete treatment of linear algebra of R² and R³ that goes in-depth
• We present in detail particular cases of all important concepts and methods from the core topics in a first course in linear algebra such as linear independence, basis, dimension, determinant, orthogonality, the least square method, eigenvalues, eigenvectors, diagonalization, and quadratic forms
• The book is easy to read and improves the results of the tests of the students, as shown since 1997 at the University of Borås, Sweden
• Students can start off by reading any chapter she or he is interested in or pick up any topic from the book with ease