Linear Algebra: Algorithms, Applications, and Techniques, Fourth Edition offers a modern and algorithmic approach to computation while providing clear and straightforward theoretical background information. The book guides readers through the major applications, with chapters on properties of real numbers, proof techniques, matrices, vector spaces, linear transformations, eigen values, and Euclidean inner products. Appendices on Jordan canonical forms and Markov chains are included for further study. This useful textbook presents broad and balanced views of theory, with key material highlighted and summarized in each chapter. To further support student practice, the book also includes ample exercises with answers and hints.
1. Linear Algebra - p. i 2. Cover - p. i 3. Title Page - p. ii 4. Copyright - p. iv 5. Table of Contents - p. iv 6. Preface - p. ix 7. Author Bio - p. xi 8. 0 Fundamentals - p. 1 9. 1 Matrices - p. 9 10. 1.1: Basic concepts - p. 9 11. 1.2: Matrix multiplication - p. 19 12. 1.3: Special matrices - p. 31 13. 1.4: Linear systems of equations - p. 38 14. 1.5: Determinants - p. 56 15. 1.6: The inverse - p. 77 16. 1.7: LU decomposition - p. 93 17. Chapter 1 review - p. 101 18. 2 Vector spaces - p. 105 19. 2.1: Properties of ℝn - p. 105 20. 2.2: Vectors - p. 121 21. 2.3: Subspaces - p. 127 22. 2.4: Linear independence - p. 137 23. 2.5: Basis and dimension - p. 146 24. 2.6: Row space of a matrix - p. 161 25. 2.7: Rank of a matrix - p. 171 26. Chapter 2 Review - p. 181 27. 3 Linear transformations - p. 185 28. 3.1: Functions - p. 185 29. 3.2: Linear transformations - p. 191 30. 3.3: Matrix representations - p. 200 31. 3.4: Change of basis - p. 213 32. 3.5: Properties of linear transformations - p. 226 33. Chapter 3 Review - p. 241 34. 4 Eigenvalues and eigenvectors - p. 243 35. 4.1: Eigenvectors and eigenvalues - p. 243 36. 4.2: Properties of eigenvalues and eigenvectors - p. 257 37. 4.3: Diagonalization of matrices - p. 263 38. 4.4: Power methods - p. 272 39. Chapter 4 review - p. 282 40. 5 Applications of eigenvalues: Differential equations - p. 285 41. 5.1: The exponential matrix - p. 285 42. 5.2: Differential equations in fundamental form - p. 298 43. 5.3: Solving differential equations in fundamental form - p. 305 44. 5.4: Modeling and differential equations - p. 315 45. Chapter 5 Review - p. 317 46. 6 Applications of eigenvalues: Graph theory - p. 319 47. 7 Euclidean inner product - p. 339 48. 7.1: Orthogonality - p. 339 49. 7.2: Projections and Gram-Schmidt orthonormalization - p. 351 50. 7.3: The QR algorithm - p. 365 51. 7.4: Least squares - p. 374 52. 7.5: Orthogonal complements - p. 383 53. Chapter 7 review - p. 391 54. Appendix A Jordan canonical forms - p. 393 55. Appendix B Markov chains - p. 427 56. Answers and hints to selected problems - p. 439 57. Index - p. 513
Linear Algebra: Algorithms, Applications, and Techniques, Fourth Edition offers a modern and algorithmic approach to computation while providing clear and straightforward theoretical background information. The book guides readers through the major applications, with chapters on properties of real numbers, proof techniques, matrices, vector spaces, linear transformations, eigen values, and Euclidean inner products. Appendices on Jordan canonical forms and Markov chains are included for further study. This useful textbook presents broad and balanced views of theory, with key material highlighted and summarized in each chapter. To further support student practice, the book also includes ample exercises with answers and hints.
1. Linear Algebra - p. i 2. Cover - p. i 3. Title Page - p. ii 4. Copyright - p. iv 5. Table of Contents - p. iv 6. Preface - p. ix 7. Author Bio - p. xi 8. 0 Fundamentals - p. 1 9. 1 Matrices - p. 9 10. 1.1: Basic concepts - p. 9 11. 1.2: Matrix multiplication - p. 19 12. 1.3: Special matrices - p. 31 13. 1.4: Linear systems of equations - p. 38 14. 1.5: Determinants - p. 56 15. 1.6: The inverse - p. 77 16. 1.7: LU decomposition - p. 93 17. Chapter 1 review - p. 101 18. 2 Vector spaces - p. 105 19. 2.1: Properties of ℝn - p. 105 20. 2.2: Vectors - p. 121 21. 2.3: Subspaces - p. 127 22. 2.4: Linear independence - p. 137 23. 2.5: Basis and dimension - p. 146 24. 2.6: Row space of a matrix - p. 161 25. 2.7: Rank of a matrix - p. 171 26. Chapter 2 Review - p. 181 27. 3 Linear transformations - p. 185 28. 3.1: Functions - p. 185 29. 3.2: Linear transformations - p. 191 30. 3.3: Matrix representations - p. 200 31. 3.4: Change of basis - p. 213 32. 3.5: Properties of linear transformations - p. 226 33. Chapter 3 Review - p. 241 34. 4 Eigenvalues and eigenvectors - p. 243 35. 4.1: Eigenvectors and eigenvalues - p. 243 36. 4.2: Properties of eigenvalues and eigenvectors - p. 257 37. 4.3: Diagonalization of matrices - p. 263 38. 4.4: Power methods - p. 272 39. Chapter 4 review - p. 282 40. 5 Applications of eigenvalues: Differential equations - p. 285 41. 5.1: The exponential matrix - p. 285 42. 5.2: Differential equations in fundamental form - p. 298 43. 5.3: Solving differential equations in fundamental form - p. 305 44. 5.4: Modeling and differential equations - p. 315 45. Chapter 5 Review - p. 317 46. 6 Applications of eigenvalues: Graph theory - p. 319 47. 7 Euclidean inner product - p. 339 48. 7.1: Orthogonality - p. 339 49. 7.2: Projections and Gram-Schmidt orthonormalization - p. 351 50. 7.3: The QR algorithm - p. 365 51. 7.4: Least squares - p. 374 52. 7.5: Orthogonal complements - p. 383 53. Chapter 7 review - p. 391 54. Appendix A Jordan canonical forms - p. 393 55. Appendix B Markov chains - p. 427 56. Answers and hints to selected problems - p. 439 57. Index - p. 513
