Note: Each chapter concludes with a Chapter Summary, Review Exercises, and Projects. What Is Linear Algebra? | |

Systems of Linear Equations Biographical Sketch of Carl Friedrich Gauss | |

Introduction to Systems of Linear Equations | |

Gaussian Elimination and Gauss-Jordan Elimination | |

Applications of Systems of Linear Equations | |

Matrices Biographical Sketch of Arthur Cayley | |

Operations with Matrices | |

Properties of Matrix Operations | |

The Inverse of a Matrix | |

Elementary Matrices | |

Applications of Matrix Operations | |

Determinants Biographical Sketch of Augustin-Louis Cauchy | |

The Determinant of a Matrix | |

Evaluation of a Determinant Using Elementary Operations | |

Properties of Determinants | |

Introduction to Eigenvalues | |

Applications of Determinants Cumulative Test for Chapters 1–3 | |

Vector Spaces Biographical Sketch of William Rowan Hamilton | |

Vectors in Rn | |

Vector Spaces | |

Subspaces of Vector Spaces | |

Spanning Sets and Linear Independence | |

Basis and Dimension | |

Rank of a Matrix and Systems of Linear Equations | |

Coordinates and Change of Basis | |

Applications of Vector Spaces | |

Inner Product Spaces Biographical Sketch of Jean-Baptiste Joseph Fourier | |

Length and Dot Product in Rn | |

Inner Product Spaces | |

Orthonormal Bases: Gram-Schmidt Process | |

Mathematical Models and Least Squares Analysis | |

Applications of Inner Product Spaces Cumulative Test for Chapters 4 and 5 | |

Linear Transformations Biographical Sketch of Emmy Noether | |

Introduction to Linear Transformations | |

The Kernel and Range of a Linear Transformation | |

Matrices for Linear Transformations | |

Transition Matrices and Similarity | |

Applications of Linear Transformations | |

Eigenvalues and Eigenvectors Biographical Sketch of James Joseph Sylvester | |

Eigenvalues and Eigenvectors | |

Diagonalization | |

Symmetric Matrices and Orthogonal Diagonalization | |

Applications of Eigenvalues and Eigenvectors Cumulative Test for Chapters 6 and 7 | |

Complex Vector Spaces* Biographical Sketch of Charles Hermite | |

Complex Numbers | |

Conjugates and Division of Complex Numbers | |

Polar Form and DeMoivre's Theorem | |

Complex Vector Spaces and Inner Products | |

Unitary and Hermitian Matrices | |

Linear Programming* Biographical Sketch of John von Neumann | |

Systems of Linear Inequalities | |

Linear Programming Involving Two Variables | |

The Simplex Method: Maximization | |

The Simplex Method: Minimization | |

The Simplex Method: Mixed Constraints | |

Numerical Methods | |

Biographical Sketch of Carl Gustav Jacob Jacobi | |

Gaussian Elimination with Partial Pivoting | |

Interative Methods for Solving Linear Systems | |

Power Method for Approximating Eigenvalues | |

Applications of Numerical Methods | |

Appendices | |

Mathematical Induction and Other Forms of Proofs | |

Computer Algebra Systems and Graphing Calculators | |

Answer Key Index * Chapters 8, 9, and 10 are available on the Learning Tools Student CD-ROM and the textbook web site | |

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