Linear Algebra with Applications

Description

Prepare for conceptual thinking in an abstract setting as Linear Algebra with Applications blends computational and conceptual topics through a large assortment of examples to improve your comfort with the rigors of the subject matter. Title Copyright Dedication Contents Preface Acknowledgments 1 Systems of Linear Equations 1.1 Lines and Linear Equations 1.2 Linear Systems and Matrices 1.3 Applications of Linear Systems* 1.4 Numerical Solutions* Supplementary Exercises 2 Euclidean Space 2.1 Vectors 2.2 Span 2.3 Linear Independence Supplementary Exercises 3 Matrices 3.1 Linear Transformations 3.2 Matrix Algebra 3.3 Inverses 3.4 LU Factorization* 3.5 Markov Chains* Supplementary Exercises 4 Subspaces 4.1 Introduction to Subspaces 4.2 Basis and Dimension 4.3 Row and Column Spaces 4.4 Change of Basis* Supplementary Exercises 5 Determinants 5.1 The Determinant Function 5.2 Properties of the Determinant 5.3 Applications of the Determinant* Supplementary Exercises 6 Eigenvalues and Eigenvectors 6.1 Eigenvalues and Eigenvectors 6.2 Diagonalization 6.3 Complex Eigenvalues and Eigenvectors* 6.4 Systems of Differential Equations* 6.5 Approximation Methods* Supplementary Exercises 7 Vector Spaces 7.1 Vector Spaces and Subspaces 7.2 Span and Linear Independence 7.3 Basis and Dimension Supplementary Exercises 8 Orthogonality 8.1 Dot Products and Orthogonal Sets 8.2 Projection and the Gram–Schmidt Process 8.3 Diagonalizing Symmetric Matrices and QR Factorization 8.4 The Singular Value Decomposition* 8.5 Least Squares Regression* Supplementary Exercises 9 Linear Transformations 9.1 Definition and Properties 9.2 Isomorphisms 9.3 The Matrix of a Linear Transformation 9.4 Similarity Supplementary Exercises 10 Inner Product Spaces 10.1 Inner Products 10.2 The Gram–Schmidt Process Revisited 10.3 Applications of Inner Products* Supplementary Exercises 11 Additional Topics and Applications* 11.1 Quadratic Forms 11.2 Positive Definite Matrices 11.3 Constrained Optimization 11.4 Complex Vector Spaces 11.5 Hermitian Matrices Supplementary Exercises Glossary Solutions to Practice Problems Answers to Selected Exercises Index Applications Index