Linear Algebra with Applications

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