Linear Algebra With Applications
ISBN: 9780136009290 | 0136009298
Edition: 8thFormat: Hardcover
Publisher: Pearson
Pub. Date: 8/26/2009
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This book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite. This thorough and accessible textfrom one of the leading figures in the use of technology in linear algebragives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important ... MORE
| Preface | |
| What's New in the Eighth Edition? | |
| Computer Exercises | |
| Overview of Text | |
| Suggested Course Outlines | |
| Supplementary Materials | |
| Acknowledgments | |
| Matrices and Systems of Equations | |
| Systems of Linear Equations | |
| Row Echelon Form | |
| Matrix Arithmetic | |
| Matrix A... MORE | |
| Elementary Matrices | |
| Partitioned Matrices | |
| Matlab Exercises | |
| Chapter Test A | |
| Chapter Test B | |
| Determinants | |
| The Determinant of a Matrix | |
| Properties of Determinants | |
| Additional Topics and Applications | |
| Matlab Exercises | |
| Chapter Test A | |
| Chapter Test B | |
| Vector Spaces | |
| Definition and Examples | |
| Subspaces | |
| Linear Independence | |
| Basis and Dimension | |
| Change of Basis | |
| Row Space and Column Space | |
| Matlab Exercises | |
| Chapter Test A | |
| Chapter Test B | |
| Linear Transformations | |
| Definition and Examples | |
| Matrix Representations of Linear Transformations | |
| Similarity | |
| Matlab Exercises | |
| Chapter Test A | |
| Chapter Test B | |
| Orthogonality | |
| The Scalar Product in Rn | |
| Orthogonal Subspaces | |
| Least Squares Problems | |
| Inner Product Spaces | |
| Orthonormal Sets | |
| The Gram-Schmidt Orthogonalization Process | |
| Orthogonal Polynomials | |
| Matlab Exercises | |
| Chapter Test A | |
| Chapter Test B | |
| Eigenvalues | |
| Eigenvalues and Eigenvectors | |
| Systems of Linear Differential Equations | |
| Diagonalization | |
| Hermitian Matrices | |
| The Singular Value Decomposition | |
| Quadratic Forms | |
| Positive Definite Matrices | |
| Nonnegative Matrices | |
| Matlab Exercises | |
| Chapter Test A | |
| Chapter Test B | |
| Numerical Linear Algebra | |
| Floating-Point Numbers | |
| Gaussian Elimination | |
| Pivoting Strategies | |
| Matrix Norms and Condition Numbers | |
| Orthogonal Transformations | |
| The Eigenvalue Problem | |
| Least Squares Problems | |
| Matlab Exercises | |
| Chapter Test A | |
| Chapter Test B | |
| Appendix: MATLAB | |
| The MATLAB Desktop Display | |
| Basic Data Elements | |
| Submatrices | |
| Generating Matrices | |
| Matrix Arithmetic | |
| MATLAB Functions | |
| Programming Features | |
| M-files | |
| Relational and Logical Operators | |
| Columnwise Array Operators | |
| Graphics | |
| Symbolic Toolbox | |
| Help Facility | |
| Conclusions | |
| Bibliography | |
| Linear Algebra and Matrix Theory | |
| Applied and Numerical Linear Algebra | |
| Books of Related Interest | |
| Answers to Selected Exercises | |
| Table of Contents provided by Publisher. All Rights Reserved. |
Steven J. Leon is a Chancellor Professor of Mathematics at the University of Massachusetts Dartmouth. He has been a Visiting Professor at Stanford University, ETH Zurich (the Swiss Federal Institute of Technology), KTH (the Royal Institute of Technology in Stockholm), UC San Diego, and Brown University. His areas of specialty are linear algebra and numerical analysis.
Leon is currently serving as Chair of the Education Committee of the International Linear Algebra Society and as Contributing Editor to Image, the Bulletin of the International Linear Algebra Society. He had previously served as Editor-in-Chief of Image from 1989 to 1997. In the 1990’s he also served as Director of the NSF sponsored ATLAST Project (Augmenting the Teaching of Linear Algebra using Software Tools). The project conducted 18 regional faculty workshops during the period from 1992–1997.
