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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 2500 exercises, covering computational and conceptual topics over a range of difficulty levels.
Jeff Holt has a B.A. from Humboldt State University and a Ph.D. from the University of Texas. He has been teaching mathematics for over 20 years, the last eleven at the University of Virginia. He currently has a joint appointment in the Department of Mathematics and the Department of Statistics at UVA.
During his career, Holt has won several awards for teaching. He has had NSF grants to support student math and science scholarships, the implementation of a computer-based homework system, and the development of an innovative undergraduate number theory course which later was turned into the text, Discovering Number Theory, coauthored with John Jones. In his spare time he enjoys lowering the value of his house with do-it-yourself home-improvement projects.
Table of Contents
Preface 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 2. Euclidean Space 2.1 Vectors 2.2 Span 2.3 Linear Independence 3. Matrices 3.1 Linear Transformations 3.2 Matrix Algebra 3.3 Inverses 3.4 LU Factorization 3.5 Markov Chains 4. Subspaces 4.1 Introduction to Subspaces 4.2 Basis and Dimension 4.3 Row and Column Spaces 4.4 Change of Basis 5. Determinants 5.1 The Determinant Function 5.2 Properties of the Determinant 5.3 Applications of the Determinant 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 7. Vector Spaces 7.1 Vector Spaces and Subspaces 7.2 Span and Linear Independence 7.3 Basis and Dimension 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 9. Linear Transformations 9.1 Definition and Properties 9.2 Isomorphisms 9.3 The Matrix of a Linear Transformation 9.4 Similarity 10. Inner Product Spaces 10.1 Inner Products 10.2 The Gram-Schmidt Process Revisited 10.3 Applications of Inner Products 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 Glossary Answers to Selected Exercises Index