Linear Algebra with Applications

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 Holt's Linear Algebra with Applications, Second Edition, blends computational and conceptual topics throughout to prepare students for the rigors of conceptual thinking in an abstract setting. The early treatment of conceptual topics in the context of Euclidean space gives students more time, and a familiar setting, in which to absorb them. This organization also makes it possible to treat eigenvalues and eigenvectors earlier than in most texts. Abstract vector spaces are introduced later, once students have developed a solid conceptual foundation. Concepts and topics are frequently accompanied by applications to provide context and motivation. Because many students learn by example, Linear Algebra with Applications provides a large number of representative examples, over and above those used to introduce topics. The text also has over 3000 exercises, covering computational and conceptual topics over a range of difficulty levels Now in its 2nd edition, Linear Algebra with Applications blends computational and conceptual topics to prepare students for the rigors of conceptual thinking in an abstract setting.