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| Note: Each chapter concludes with a Chapter Summary, Review Exercises, and Projects. What Is Linear Algebra? | |
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| Systems of Linear Equations Biographical Sketch of Carl Friedrich Gauss | |
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| Introduction to Systems of Linear Equations | |
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| Gaussian Elimination and Gauss-Jordan Elimination | |
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| Applications of Systems of Linear Equations | |
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| Matrices Biographical Sketch of Arthur Cayley | |
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| Operations with Matrices | |
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| Properties of Matrix Operations | |
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| The Inverse of a Matrix | |
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| Elementary Matrices | |
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| Applications of Matrix Operations | |
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| Determinants Biographical Sketch of Augustin-Louis Cauchy | |
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| The Determinant of a Matrix | |
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| Evaluation of a Determinant Using Elementary Operations | |
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| Properties of Determinants | |
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| Introduction to Eigenvalues | |
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| Applications of Determinants Cumulative Test for Chapters 13 | |
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| Vector Spaces Biographical Sketch of William Rowan Hamilton | |
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| Vectors in Rn | |
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| Vector Spaces | |
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| Subspaces of Vector Spaces | |
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| Spanning Sets and Linear Independence | |
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| Basis and Dimension | |
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| Rank of a Matrix and Systems of Linear Equations | |
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| Coordinates and Change of Basis | |
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| Applications of Vector Spaces | |
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| Inner Product Spaces Biographical Sketch of Jean-Baptiste Joseph Fourier | |
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| Length and Dot Product in Rn | |
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| Inner Product Spaces | |
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| Orthonormal Bases: Gram-Schmidt Process | |
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| Mathematical Models and Least Squares Analysis | |
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| Applications of Inner Product Spaces Cumulative Test for Chapters 4 and 5 | |
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| Linear Transformations Biographical Sketch of Emmy Noether | |
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| Introduction to Linear Transformations | |
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| The Kernel and Range of a Linear Transformation | |
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| Matrices for Linear Transformations | |
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| Transition Matrices and Similarity | |
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| Applications of Linear Transformations | |
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| Eigenvalues and Eigenvectors Biographical Sketch of James Joseph Sylvester | |
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| Eigenvalues and Eigenvectors | |
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| Diagonalization | |
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| Symmetric Matrices and Orthogonal Diagonalization | |
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| Applications of Eigenvalues and Eigenvectors Cumulative Test for Chapters 6 and 7 | |
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| Complex Vector Spaces* Biographical Sketch of Charles Hermite | |
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| Complex Numbers | |
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| Conjugates and Division of Complex Numbers | |
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| Polar Form and DeMoivre's Theorem | |
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| Complex Vector Spaces and Inner Products | |
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| Unitary and Hermitian Matrices | |
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| Linear Programming* Biographical Sketch of John von Neumann | |
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| Systems of Linear Inequalities | |
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| Linear Programming Involving Two Variables | |
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| The Simplex Method: Maximization | |
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| The Simplex Method: Minimization | |
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| The Simplex Method: Mixed Constraints | |
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| Numerical Methods | |
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| Biographical Sketch of Carl Gustav Jacob Jacobi | |
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| Gaussian Elimination with Partial Pivoting | |
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| Interative Methods for Solving Linear Systems | |
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| Power Method for Approximating Eigenvalues | |
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| Applications of Numerical Methods | |
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| Appendices | |
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| Mathematical Induction and Other Forms of Proofs | |
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| Computer Algebra Systems and Graphing Calculators | |
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| Answer Key Index * Chapters 8, 9, and 10 are available on the Learning Tools Student CD-ROM and the textbook web site | |