Linear Algebra with Applications

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 text, from one of the leading figures in the use of technology in linear algebra, gives 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 roles geometry and visualization play in understanding linear algebra.Preface What's New in the Eighth Edition? Computer Exercises Overview of Text Suggested Course Outlines Supplementary Materials Acknowledgments 1. Matrices and Systems of Equations 1.1 Systems of Linear Equations 1.2 Row Echelon Form 1.3 Matrix Arithmetic 1.4 Matrix Algebra 1.5 Elementary Matrices 1.6 Partitioned Matrices Matlab Exercises Chapter Test A Chapter Test B 2. Determinants 2.1 The Determinant of a Matrix 2.2 Properties of Determinants 2.3 Additional Topics and Applications Matlab Exercises Chapter Test A Chapter Test B 3. Vector Spaces 3.1 Definition and Examples 3.2 Subspaces 3.3 Linear Independence 3.4 Basis and Dimension 3.5 Change of Basis 3.6 Row Space and Column Space Matlab Exercises Chapter Test A Chapter Test B 4. Linear Transformations 4.1 Definition and Examples 4.2 Matrix Representations of Linear Transformations 4.3 Similarity Matlab Exercises Chapter Test A Chapter Test B 5. Orthogonality 5.1 The Scalar Product in Rn 5.2 Orthogonal Subspaces 5.3 Least Squares Problems 5.4 Inner Product Spaces 5.5 Orthonormal Sets 5.6 The Gram-Schmidt Orthogonalization Process 5.7 Orthogonal Polynomials Matlab Exercises Chapter Test A Chapter Test B 6. Eigenvalues 6.1 Eigenvalues and Eigenvectors 6.2 Systems of Linear Differential Equations 6.3 Diagonalization 6.4 Hermitian Matrices 6.5 The Singular Value Decomposition 6.6 Quadratic Forms 6.7 Positive Definite Matrices 6.8 Nonnegative Matrices Matlab Exercises Chapter Test A Chapter Test B 7. Numerical Linear Algebra 7.1 Floating-Point Numbers 7.2 Gaussian Elimination 7.3 Pivoting Strategies 7.4 Matrix Norms and Condition Numbers 7.5 Orthogonal Transformations 7.6 The Eigenvalue Problem 7.7 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 A. Linear Algebra and Matrix Theory B. Applied and Numerical Linear Algebra C. Books of Related Interest Answers to Selected Exercises