## Book description

Ward Cheney and David Kincaid have developed Linear Algebra: Theory and Applications, Second Edition, a multi-faceted introductory textbook, which was motivated by their desire for a single text that meets the various requirements for differing courses within linear algebra. For theoretically-oriented students, the text guides them as they devise proofs and deal with abstractions by focusing on a comprehensive blend between theory and applications. For application-oriented science and engineering students, it contains numerous exercises that help them focus on understanding and learning not only vector spaces, matrices, and linear transformations, but also how software tools are used in applied linear algebra. Using a flexible design, it is an ideal textbook for instructors who wish to make their own choice regarding what material to emphasize, and to accentuate those choices with homework assignments from a large variety of exercises, both in the text and online.

1. The Jones & Bartlett Learning Series in Mathematics
2. The Jones & Bartlett Learning International Series in Mathematics
3. Contents
4. Preface
5. CHAPTER ONE Systems of Linear Equations
1. 1.1 SOLVING SYSTEMS OF LINEAR EQUATIONS
2. 1.2 VECTORS AND MATRICES
3. 1.3 KERNELS, RANK, HOMOGENEOUS EQUATIONS
6. CHAPTER TWO Vector Spaces
1. 2.1 EUCLIDEAN VECTOR SPACES
2. 2.2 LINES, PLANES, AND HYPERPLANES
3. 2.3 LINEAR TRANSFORMATIONS
4. 2.4 GENERAL VECTOR SPACES
7. CHAPTER THREE Matrix Operations
1. 3.1 MATRICES
2. COMPUTER EXERCISES 3.1
3. 3.2 MATRIX INVERSES
4. SUMMARY 3.2
5. KEY CONCEPTS 3.2
6. GENERAL EXERCISES 3.2
7. COMPUTER EXERCISES 3.2
8. CHAPTER FOUR Determinants
1. 4.1 DETERMINANTS: INTRODUCTION
2. 4.2 DETERMINANTS: PROPERTIES
9. CHAPTER FIVE Vector Subspaces
1. 5.1 COLUMN, ROW, AND NULL SPACES
2. 5.2 BASES AND DIMENSION
3. 5.3 COORDINATE SYSTEMS
10. CHAPTER SIX Eigensystems
1. 6.1 EIGENVALUES AND EIGENVECTORS
11. CHAPTER SEVEN Inner -Product Vector Spaces
1. 7.1 INNER-PRODUCT SPACES“
2. 7.2 ORTHOGONALITY
1. 8.1 HERMITIAN MATRICES AND THE SPECTRAL THEOREM
2. 8.2 MATRIX FACTORIZATIONS AND BLOCK MATRICES
3. 8.3 ITERATIVE METHODS FOR LINEAR EQUATIONS
13. APPENDIX A Deductive Reasoning and Proofs
1. A.1 Introduction
2. A.2 Deductive Reasoning and Direct Verification
3. A.3 Implications
5. A.5 Mathematical Induction
6. A.6 Truth Tables
7. A.7 Subsets and de Morgan Laws
8. A.8 Quantifiers
9. A.9 Denial of a Quantified Assertion
10. A.10 Some More Questionable ‘‘Proofs’’
14. APPENDIX B Complex Arithmetic