Linear Algebra : Theory and Applications
Ward Cheney & David Kincaid
Jones and Bartlett
Table of Contents
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Chapter 1. Systems of Linear Equations
1.1 Solving Linear Systems
1.2 Vectors and Matrices
1.3 Homogeneous Linear Systems
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Chapter 2. Vector Spaces and Transformations
2.1 Euclidean Vector Spaces
2.2 Line, Planes, and More
2.3 Linear Transformations
2.4 General Vector Spaces
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Chapter 3. Matrix Operations
3.1 Matrices
3.2 Matrix Inverses
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Chapter 4. Determinants
4.1 Determinants: Introduction
4.2 Determinants: Properties and Applications
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Chapter 5. Vector Spaces
5.1 Column, Row, and Null Spaces
5.2 Bases and Dimension
5.3 Coordinate Systems
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Chapter 6. Eigensystems
6.1 Eigenvalues and Eigenvectors
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Chapter 7. Inner Product Vector Spaces
7.1 Inner Product Spaces
7.2 Orthogonality
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Chapter 8. Additional Topics
8.1 Hermitian Matrices and Spectral Theorem
8.2 Matrix Factorizations and Block Matrices
8.3 Iterative Methods
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Appendix A. Deductive Reasoning, Proofs
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Appendix B. Complex Arithmetic
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Answers and Hints to Selected Problems
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References