Linear Algebra with Applications 2nd edition by Jeffrey Holt – Ebook PDF Instant Download/Delivery: 1319057695, 9781319057695
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ISBN 10: 1319057695
ISBN 13: 9781319057695
Author: Jeffrey Holt
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.
Linear Algebra with Applications 2nd Table of contents:
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
Solutions to Practice Problems
Answers to Selected Exercises
Index
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Tags: Jeffrey Holt, Linear Algebra, Applications