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.
- Introduces deductive reasoning and helps the reader develop a facility with mathematical proofs
- Provides a balanced approach to computation and theory by offering computational algorithms for finding eigenvalues and eigenvectors
- Offers excellent exercise sets, ranging from drill to theoretical/challenging, along with useful and interesting applications not found in other introductory linear algebra texts
| Preface |
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ix | |
| Author Bio |
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xi | |
| Fundamentals |
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1 | (8) |
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0.1 Basic properties of real numbers |
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1 | (1) |
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0.2 Propositions and conditional statements |
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2 | (1) |
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3 | (1) |
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0.4 Proof by contrapositive |
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4 | (1) |
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0.5 Proof by contradiction |
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5 | (1) |
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0.6 Mathematical induction |
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6 | (3) |
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9 | (96) |
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9 | (10) |
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1.2 Matrix multiplication |
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19 | (12) |
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31 | (9) |
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1.4 Linear systems of equations |
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40 | (17) |
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57 | (20) |
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77 | (16) |
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93 | (12) |
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101 | (4) |
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105 | (80) |
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105 | (10) |
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115 | (12) |
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127 | (10) |
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137 | (9) |
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146 | (15) |
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2.6 Row space of a matrix |
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161 | (10) |
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171 | (14) |
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181 | (4) |
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185 | (58) |
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185 | (6) |
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3.2 Linear transformations |
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191 | (9) |
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3.3 Matrix representations |
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200 | (13) |
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213 | (13) |
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3.5 Properties of linear transformations |
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226 | (17) |
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241 | (2) |
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4 Eigenvalues and eigenvectors |
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243 | (42) |
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4.1 Eigenvectors and eigenvalues |
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243 | (14) |
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4.2 Properties of eigenvalues and eigenvectors |
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257 | (6) |
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4.3 Diagonalization of matrices |
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263 | (9) |
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272 | (13) |
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282 | (3) |
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5 Applications of eigenvalues: Differential equations |
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285 | (34) |
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5.1 The exponential matrix |
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285 | (13) |
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5.2 Differential equations in fundamental form |
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298 | (7) |
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5.3 Solving differential equations in fundamental form |
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305 | (10) |
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5.4 Modeling and differential equations |
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315 | (4) |
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318 | (1) |
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6 Applications of eigenvalues: Graph theory |
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319 | (20) |
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6.1 A brief introduction to graphs and networks |
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319 | (1) |
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320 | (6) |
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326 | (5) |
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6.4 Adjacency matrix eigenvalues |
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331 | (8) |
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337 | (2) |
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7 Euclidean inner product |
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339 | (54) |
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339 | (12) |
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7.2 Projections and Gram-Schmidt orthonormalization |
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351 | (14) |
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365 | (9) |
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374 | (9) |
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7.5 Orthogonal complements |
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383 | (10) |
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391 | (2) |
| Appendix A Jordan canonical forms |
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393 | (34) |
| Appendix B Markov chains |
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427 | (12) |
| Answers and hints to selected problems |
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439 | (74) |
| Index |
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513 | |
Richard Bronson is a Professor of Mathematics and Computer Science at Fairleigh Dickinson University and is Senior Executive Assistant to the President. Ph.D., in Mathematics from Stevens Institute of Technology. He has written several books and numerous articles on Mathematics. He has served as Interim Provost of the Metropolitan Campus, and has been Acting Dean of the College of Science and Engineering at the university in New Jersey Gabriel B. Costa is currently a visiting professor at the United States Military Academy at West Point and is on the faculty at Seton Hall. And is an engineer. He holds many titles and fills them with distinction. He has a B.S., M.S. and Ph.D. in Mathematics from Stevens Institute of Technology. He has also co-authored another Academic Press book with Richard Bronson, Matrix Methods. John T. Saccoman is Professor and Chair, Department of Mathematics and Computer Science, Seton Hall University, New Jersey received Ph.D., Stevens Institute of Technology, Hoboken, NJ, 1995 Research work on synthesis results in network reliability theory. He has published in several journals, authored supplementary materials, and is highly involved in the use of technology in applied mathematics. He has worked collaboratively on writings for Transforming the Curriculum Across the Disciplines Through Technology-Based Faculty Development and Writing-Intensive Course Redesign. Daniel Gross is a professor in the Department of Mathematics and Computer Science at Seton Hall University in South Orange, New Jersey. Dan received his PhD in Mathematics from the University of Notre Dame in 1982. His research interests are network reliability and network vulnerability.
