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Linear Algebra with Applications
ISBN: 9780131857858 | 0131857851
Edition: 8thFormat: Hardcover
Publisher: Prentice Hall
Pub. Date: 1/1/2010
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This thorough and accessible book from one of the leading figures in the field of linear algebra provides readers with both a challenging and broad understanding of linear algebra. The author infuses key concepts with their modern practical applications to offer readers examples of how mathematics is used in the real world. Topics such as linear systems theory, matrix theory, and vector space theory are integrated with real world applications to give a clear understanding of the material and the application of the concepts to solve real world p... MORE
| Preface | p. ix |
| Matrices and Systems of Equations | p. 1 |
| Systems of Linear Equations | p. 1 |
| Row Echelon Form | p. 13 |
| Matrix Algebra | p. 33 |
| Elementary Matrices | p. 67 |
| Partitioned Matrices | p. 79 |
| Matlab Exercises | p. 91 |
| Chapter Test | p. 97 |
| Determinants | p. 99 |
| The Determinant of a Matrix | p. 99... MORE |
| Properties of Determinants | p. 107 |
| Cramer's Rule | p. 115 |
| Matlab Exercises | p. 121 |
| Chapter Test | p. 123 |
| Vector Spaces | p. 125 |
| Definition and Examples | p. 125 |
| Subspaces | p. 134 |
| Linear Independence | p. 144 |
| Basis and Dimension | p. 156 |
| Change of Basis | p. 163 |
| Row Space and Column Space | p. 174 |
| Matlab Exercises | p. 184 |
| Chapter Test | p. 186 |
| Linear Transformations | p. 188 |
| Definition and Examples | p. 188 |
| Matrix Representations of Linear Transformations | p. 198 |
| Similarity | p. 212 |
| Matlab Exercises | p. 220 |
| Chapter Test | p. 221 |
| Orthogonality | p. 223 |
| The Scalar Product in R[superscript n] | p. 224 |
| Orthogonal Subspaces | p. 239 |
| Least Squares Problems | p. 249 |
| Inner Product Spaces | p. 260 |
| Orthonormal Sets | p. 270 |
| The Gram--Schmidt Orthogonalization Process | p. 290 |
| Orthogonal Polynomials | p. 299 |
| Matlab Exercises | p. 307 |
| Chapter Test | p. 310 |
| Eigenvalues | p. 312 |
| Eigenvalues and Eigenvectors | p. 313 |
| Systems of Linear Differential Equations | p. 326 |
| Diagonalization | p. 339 |
| Hermitian Matrices | p. 355 |
| The Singular Value Decomposition | p. 367 |
| Quadratic Forms | p. 382 |
| Positive Definite Matrices | p. 397 |
| Nonnegative Matrices | p. 405 |
| Matlab Exercises | p. 412 |
| Chapter Test | p. 421 |
| Numerical Linear Algebra | p. 422 |
| Floating-Point Numbers | p. 423 |
| Gaussian Elimination | p. 427 |
| Pivoting Strategies | p. 436 |
| Matrix Norms and Condition Numbers | p. 442 |
| Orthogonal Transformations | p. 458 |
| The Eigenvalue Problem | p. 470 |
| Least Squares Problems | p. 482 |
| Matlab Exercises | p. 494 |
| Chapter Test | p. 503 |
| Iterative Methods *Web | |
| Jordan Canonical Form *Web | |
| Matlab | p. 505 |
| Bibliography | p. 517 |
| Answers to Selected Exercises | p. 520 |
| Index | p. 540 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
