Matrix Methods: Applied Linear Algebra and Sabermetrics, Fourth Edition, provides a unique and comprehensive balance between the theory and computation of matrices. Rapid changes in technology have made this valuable overview on the application of matrices relevant not just to mathematicians, but to a broad range of other fields. Matrix methods, the essence of linear algebra, can be used to help physical scientists-- chemists, physicists, engineers, statisticians, and economists-- solve real world problems.
1. 3.1. Introduction - p. 93 2. Problems 3.1 - p. 98 3. 3.2. Calculating inverses - p. 103 4. Problems 3.2 - p. 108 5. 3.3. Simultaneous equations - p. 112 6. Problems 3.3 - p. 114 7. 3.4. Properties of the inverse - p. 116 8. Problems 3.4 - p. 117 9. 3.5. LU decomposition - p. 118 10. Problems 3.5 - p. 124 11. 3.6. Final comments on Chapter 3 - p. 127 12. Chapter 4. An introduction to optimization - p. 131 13. Chapter 5. Determinants - p. 151 14. 5.1. Introduction - p. 151 15. Problems 5.1 - p. 153 16. 5.2. Expansion by cofactors - p. 155 17. Problems 5.2 - p. 158 18. 5.3. Properties of determinants - p. 161 19. Problems 5.3 - p. 166 20. 5.4. Pivotal condensation - p. 168 21. Problems 5.4 - p. 171 22. 5.5. Inversion - p. 173 23. Problems 5.5 - p. 176 24. 5.6. Cramer's rule - p. 177 25. Problems 5.6 - p. 180 26. 5.7. Final comments on Chapter 5 - p. 181 27. Chapter 6. Eigenvalues and eigenvectors - p. 185 28. 6.1. Definitions - p. 185 29. Problems 6.1 - p. 187 30. 6.2. Eigenvalues - p. 190 31. Problems 6.2 - p. 192 32. 6.3. Eigenvectors - p. 196 33. Problems 6.3 - p. 199 34. 6.4. Properties of eigenvalues and eigenvectors - p. 202 35. Problems 6.4 - p. 205 36. 6.5. Linearly independent eigenvectors - p. 207 37. Problems 6.5 - p. 212 38. 6.6. Power methods - p. 213 39. Problems 6.6 - p. 222 40. Chapter 7. Matrix calculus - p. 225 41. 7.1. Well-defined functions - p. 225 42. Problems 7.1 - p. 229 43. 7.2. Cayley–Hamilton theorem - p. 231 44. Problems 7.2 - p. 234 45. 7.3. Polynomials of matrices—distinct eigenvalues - p. 234 46. Problems 7.3 - p. 238 47. 7.4. Polynomials of matrices—general case - p. 240 48. Problems 7.4 - p. 243 49. 7.5. Functions of a matrix - p. 244 50. Problems 7.5 - p. 247 51. 7.6. The function eAt - p. 249 52. Problems 7.6 - p. 251 53. 7.7. Complex eigenvalues - p. 252 54. Problems 7.7 - p. 255 55. 7.8. Properties of eA - p. 255 56. Problems 7.8 - p. 258 57. 7.9. Derivatives of a matrix - p. 259 58. Problems 7.9 - p. 263 59. 7.10. Final comments on Chapter 7 - p. 264 60. Chapter 8. Linear differential equations - p. 267 61. 8.1. Fundamental form - p. 267 62. Problems 8.1 - p. 271 63. 8.2. Reduction of an nth order equation - p. 273 64. Problems 8.2 - p. 279 65. 8.3. Reduction of a system - p. 280 66. Problems 8.3 - p. 284 67. 8.4. Solutions of systems with constant coefficients - p. 285 68. Problems 8.4 - p. 294 69. 8.5. Solutions of systems—general case - p. 295 70. Problem 8.5 - p. 302 71. 8.6. Final comments on Chapter 8 - p. 303 72. Chapter 9. Probability and Markov chains - p. 305 73. Chapter 10. Real inner products and least squares - p. 323 74. 10.1. Introduction - p. 323 75. Problems 10.1 - p. 325 76. 10.2. Orthonormal vectors - p. 328 77. Problems 10.2 - p. 333 78. 10.3. Projections and QR decompositions - p. 336 79. Problems 10.3 - p. 346 80. 10.4. The QR algorithm - p. 348 81. Problems 10.4 - p. 353 82. 10.5. Least squares - p. 354 83. Problems 10.5 - p. 362 84. Chapter 11. Sabermetrics – An introduction - p. 365 85. Chapter 12. Sabermetrics – A module - p. 375 86. Appendix A. A word on technology - p. 381 87. Answers and hints to selected problems - p. 383 88. Index - p. 487
Matrix Methods: Applied Linear Algebra and Sabermetrics, Fourth Edition, provides a unique and comprehensive balance between the theory and computation of matrices. Rapid changes in technology have made this valuable overview on the application of matrices relevant not just to mathematicians, but to a broad range of other fields. Matrix methods, the essence of linear algebra, can be used to help physical scientists-- chemists, physicists, engineers, statisticians, and economists-- solve real world problems.
1. 3.1. Introduction - p. 93 2. Problems 3.1 - p. 98 3. 3.2. Calculating inverses - p. 103 4. Problems 3.2 - p. 108 5. 3.3. Simultaneous equations - p. 112 6. Problems 3.3 - p. 114 7. 3.4. Properties of the inverse - p. 116 8. Problems 3.4 - p. 117 9. 3.5. LU decomposition - p. 118 10. Problems 3.5 - p. 124 11. 3.6. Final comments on Chapter 3 - p. 127 12. Chapter 4. An introduction to optimization - p. 131 13. Chapter 5. Determinants - p. 151 14. 5.1. Introduction - p. 151 15. Problems 5.1 - p. 153 16. 5.2. Expansion by cofactors - p. 155 17. Problems 5.2 - p. 158 18. 5.3. Properties of determinants - p. 161 19. Problems 5.3 - p. 166 20. 5.4. Pivotal condensation - p. 168 21. Problems 5.4 - p. 171 22. 5.5. Inversion - p. 173 23. Problems 5.5 - p. 176 24. 5.6. Cramer's rule - p. 177 25. Problems 5.6 - p. 180 26. 5.7. Final comments on Chapter 5 - p. 181 27. Chapter 6. Eigenvalues and eigenvectors - p. 185 28. 6.1. Definitions - p. 185 29. Problems 6.1 - p. 187 30. 6.2. Eigenvalues - p. 190 31. Problems 6.2 - p. 192 32. 6.3. Eigenvectors - p. 196 33. Problems 6.3 - p. 199 34. 6.4. Properties of eigenvalues and eigenvectors - p. 202 35. Problems 6.4 - p. 205 36. 6.5. Linearly independent eigenvectors - p. 207 37. Problems 6.5 - p. 212 38. 6.6. Power methods - p. 213 39. Problems 6.6 - p. 222 40. Chapter 7. Matrix calculus - p. 225 41. 7.1. Well-defined functions - p. 225 42. Problems 7.1 - p. 229 43. 7.2. Cayley–Hamilton theorem - p. 231 44. Problems 7.2 - p. 234 45. 7.3. Polynomials of matrices—distinct eigenvalues - p. 234 46. Problems 7.3 - p. 238 47. 7.4. Polynomials of matrices—general case - p. 240 48. Problems 7.4 - p. 243 49. 7.5. Functions of a matrix - p. 244 50. Problems 7.5 - p. 247 51. 7.6. The function eAt - p. 249 52. Problems 7.6 - p. 251 53. 7.7. Complex eigenvalues - p. 252 54. Problems 7.7 - p. 255 55. 7.8. Properties of eA - p. 255 56. Problems 7.8 - p. 258 57. 7.9. Derivatives of a matrix - p. 259 58. Problems 7.9 - p. 263 59. 7.10. Final comments on Chapter 7 - p. 264 60. Chapter 8. Linear differential equations - p. 267 61. 8.1. Fundamental form - p. 267 62. Problems 8.1 - p. 271 63. 8.2. Reduction of an nth order equation - p. 273 64. Problems 8.2 - p. 279 65. 8.3. Reduction of a system - p. 280 66. Problems 8.3 - p. 284 67. 8.4. Solutions of systems with constant coefficients - p. 285 68. Problems 8.4 - p. 294 69. 8.5. Solutions of systems—general case - p. 295 70. Problem 8.5 - p. 302 71. 8.6. Final comments on Chapter 8 - p. 303 72. Chapter 9. Probability and Markov chains - p. 305 73. Chapter 10. Real inner products and least squares - p. 323 74. 10.1. Introduction - p. 323 75. Problems 10.1 - p. 325 76. 10.2. Orthonormal vectors - p. 328 77. Problems 10.2 - p. 333 78. 10.3. Projections and QR decompositions - p. 336 79. Problems 10.3 - p. 346 80. 10.4. The QR algorithm - p. 348 81. Problems 10.4 - p. 353 82. 10.5. Least squares - p. 354 83. Problems 10.5 - p. 362 84. Chapter 11. Sabermetrics – An introduction - p. 365 85. Chapter 12. Sabermetrics – A module - p. 375 86. Appendix A. A word on technology - p. 381 87. Answers and hints to selected problems - p. 383 88. Index - p. 487
