There are two aspects of linear algebra: abstract and applied. Both these aspects play important role in diverse branches of mathematics, physics, engineering, economics, and so on. The aim of this book is to present both these aspects of linear algebra. We shall try to show how abstract concepts arise out of applications and physical needs, and how abstract concepts can be applied in various problems. Normally, students are taught matrices and determinants in the first introductory course in linear algebra. We shall assume familiarity with the concept of matrices only. However, we do give a brief introduction of matrices in chapter 2. We will relate the origin and use of these concepts in linear algebra. The book contains a moderate set of exercises. We intend to bring out an interactive e-version of the book in a CDROM. A preview of the same is available on the website www.math4all. in. Contents 1. From Geometry to Algebra-I: The Euclidean Space R3, 2. Systems of Linear Equations, 3. Linear Independence and Dependence of Vectors, 4. Determinants, 5. Vector Spaces, 6. Linear Transformations, 7. From Geometry to Algebra-II: Inner Product Spaces, 8. Orthogonal Projections and Orthogonal Basis, 9. Isometries and Orthogonal Matrices, 10. Diagonalization and the Spectral Theorem, 11. Applications of Diagonalization, Answers, Index
