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| Linear Systems and Matrices | |
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| Linear Systems of Equations | |
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| Elementary Operations and Gauss Elimination Method | |
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| Homogeneous Linear Systems | |
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| Introduction to Matrices and the Matrix of a Linear System | |
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| Elementary Row Operations on a Matrix | |
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| Proofs of Facts | |
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| Chapter Review Questions and Project | |
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| Algebra of Matrices | |
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| Scalar Multiplication and Addition of Matrices | |
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| Matrix Multiplication and Its Properties | |
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| Transpose | |
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| Proofs of Facts | |
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| Chapter Review Questions and Projects | |
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| Subspaces | |
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| Linear Combination of Vectors | |
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| Vector Subspaces | |
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| Linear Dependence, Linear Independence, and Basis | |
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| Proofs of Facts | |
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| Chapter Review Questions and Project | |
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| Rank | |
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| Elementary Operations and Rank | |
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| Null Space and Nullity of a Matrix | |
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| Elementary Matrices | |
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| Proofs of Facts | |
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| Chapter Review Questions and Project | |
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| Inverse, Rank Factorization, and LU-Decomposition | |
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| Inverse of a Matrix and Its Properties | |
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| Further Properties of Inverses | |
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| Full-Rank Factorization | |
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| LU-Decomposition of a Matrix | |
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| Proofs of Facts | |
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| Chapter Review Questions and Projects | |
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| Determinants | |
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| Determinant | |
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| Properties of the Determinant | |
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| Cofactors and Inverse of a Matrix | |
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| Cramer's Rule | |
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| Chapter Review Questions and Projects | |
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| Eigenvalue Problems | |
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| Eigenvalues and Eigenvectors | |
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| Characteristic Polynomial | |
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| Calculating Eigenvalues and Eigenvectors (Another Approach) and the Cayley-Hamilton Theorem | |
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| Applications of the Cayley-Hamilton Theorem | |
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| Properties of Eigenvalues, Diagonalizability, and Triangularizability | |
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| Proofs of Facts | |
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| Chapter Review Questions and Projects | |
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| Inner Product Spaces | |
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| Gram-Schmidt Orthogonalization Process | |
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| Diagonalization of Symmetric Matrices | |
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| Application of the Spectral Theorem | |
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| Least-Squares Solution | |
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| Generalized Inverse and Least-Squares Solution | |
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| Proofs of Facts | |
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| Chapter Review Questions and Projects | |
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| Vector Spaces and Linear Mappings | |
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| Vector Spaces | |
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| Linear Dependence and Linear Independence | |
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| Linear Mappings | |
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| Some Properties of Linear Mappings: Image and Kernel | |
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| Linear Mappings and Matrices | |
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| Chapter Review Questions and Projects | |
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| Determinants (Revisited) | |
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| Permutations | |
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| Determinants | |
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| Cofactor Expansion | |
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| Adjoint of a Matrix | |
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| Cramer's Rule | |
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| Product Theorem of Determinants | |
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| Answers and Hints to Selected Exercises | |
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| Drill Solutions Using Matlab | |
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| Some Basic Matlab Operations | |
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| Index | |